In the absence of Giuseppe Rossi, Montella seems to favor a 4-3-3. This is one of the two most popular formations in the world right now (along with 4-2-3-1), and for good reason. Width is frequently a priority, as the fullbacks can come forward to overload the defense in the attack, and the wingers can drop back to help defend against opposing fullbacks in defense. If and when the fullbacks overlap, the wingers can move inside to become, in effect, extra strikers. The three midfielders in the center make ball retention easier and keep the center of the pitch protected against quick breaks through the middle. Having three attackers spread across the field makes finding a forward pass easier, since the defense has to spread out to mark them. There are two major weaknesses that I can think of. First, if the wingers or the midfielders get forced back, the striker becomes very isolated and the attack can stall out. Also, playing against two strikers can leave the defense short on numbers, as each centerback marks a striker, which leaves no spare player at the back. If both fullbacks are caught high up the pitch, the opponent can break quickly with a two-on-two.
Montella's 4-3-3 is predicated upon ball retention and creativity in the middle. He likes Pizarro in the deepest midfield spot, where he generally has lots of time to pick out a pass; of course, if he's pressured effectively, the team can struggle to move the ball forward. Given the dearth of an effective wide attacker for the left side, a more central player--usually Babacar or Ilicic this year--plays the spot, but usually comes inside. To compensate for this loss of width, Borja Valero drifts into the wide left positions and the leftback, whether Pasqual or Alonso, has to get forward as well.
This seems to be Montella's preferred formation when Rossi and Gomez are available. Popular in the late eighties and early nineties, the 3-5-2 is experiencing a renaissance, culminating in an unfancied Dutch side reaching the semifinals of the World Cup. It provides a lot of numbers in the middle, with three centerbacks, three central midfielders, and three strikers, which makes it easy to control the center of the pitch. The extra centerback is useful at set pieces, as well. Fielding two strikers can be hard on a team playing with a back four, as it will require man-to-man marking by the centerbacks, meaning that the smallest mistake can be costly. The midfield needs to be effective at linking up with the strikers, who can otherwise become isolated. Thus, among teams that play a 3-5-2, energetic players in the middle are very useful. The primary weakness is a lack of width. The wingbacks have to cope with opposing wingers and then run down the line and become wingers themselves in attack, which is extremely physically demanding. By playing with wide players high up the pitch, a team can either force the wingbacks to stay deep and defend or make the outside centerbacks move wide. The former saps the attack of width, and the latter opens massive holes in the defense.
Montella's 3-5-2 avoids many of these issues very cleverly, since it's more of a hybrid system. What sets it apart are the roles of the wingbacks. By fielding a more defensive player--ie, Pasqual or Alonso--on the left and a more attacking player--ie, Cuadrado--on the right, the back three isn't exposed as much to wide attacks, especially since the right centerback--Tomovic or Richards--is comfortable as a rightback as well. With the left wingback generally staying deeper, width on the left is achieved by Valero's drifts towards the touchline. This balance is also why I doubt we'll see a 3-5-2 with Cuadrado and Bernardeschi or Marin on the wings. Farther forward, Montella has shown a desire to play a big man and little man up front, with the former working as a target man and the latter dropping deep to link the play, which turns the formation into more a 3-5-1-1. While this allows another playmaker (Ilicic or Fernandez) to keep possession, the striker can get isolated, and it removes another threat high up the pitch to threaten the defense.
Arguably the shape England won their only World Cup in 1966, the 4-3-1-2 had its heyday in the nineties and early aughts (still can't find a less pretentious term for the years from 2000 to 2009). While it allows for control of the middle, it sacrifices attacking width. The fullbacks, as the only wide players on the field, are forced to cover a lot of ground going forward. Alternatively, the outside midfielders in the bank of three can move out wide (Schalke did this really well a few years ago) or the strikers can drift wide as well (think Prandelli's Italy in Euro 2012). All in all, it's very similar to the 3-5-2, except that the only wide players (fullbacks) start even farther back, which limits the width in attack even more. The lack of width also places the burden for creativity squarely on the trequartista; should he be off-form, the strikers are separated from the rest of the team, since there aren't any wide options directly available to help involve them. The usual strengths and weaknesses of a back four are present. The outside midfielders can tire more quickly in this shape, as they have to shuttle out wide in attack and defense. The final point is that passing forward from the midfield can be trickier as well. With all three attackers playing narrow, the opposing defense can collapse on them, making a forward pass very difficult.
In the past, this has been a desperation play by Montella, usually for when Cuadrado is unavailable. Rossi, Babacar, or Ilicic partners Gomez up front, with Ilicic or Valero as the trequartista. The left side is generally where the width is, as Valero moves that direction and Pasqual or Alonso at leftback naturally come forward more than Tomovic at rightback. The left striker also seems to spend more time out wide than the right striker, as seen by Babacar's hard-working role out wide against Roma. Against inferior competition, it's a fine formation, but a top-class side will stifle most teams in a 4-3-1-2 without much difficulty.
As Josip Ilicic's name keeps popping up here, we'll finish with the shape that made him a star with Palermo. It's a variation of the 4-3-3 in which the wingers, instead of staying wide, move inside to provide more playmaking options through the center. This allows for lots of men in the middle, although it can leave the wide areas vacant, putting the onus on fullbacks or midfielders to shuttle towards the touchlines. Similarly, if the opponent deploys attacking fullbacks, they can cause significant problems by overloading the wide areas. Otherwise, this is basically a 4-3-3, with all the aforementioned tendencies in attack and defense.
Montella, when using this shape, tends to go off-balance with it, using one true wide player, usually on the right--Cuadrado or Joaquin--along with either an inverted wide player or a more central player on the left--Cuadrado, Joaquin, or Ilicic. Given the natural tendencies of this team to keep width on the left rather than the right, this provides some balance and also some natural movement.
There are a few pretty obvious conclusions from this information. The most obvious is that Montella always has three central midfielders, and rotates the other seven outfield players around them. This indicates that controlling the center of the pitch is Montella's top priority. Since he hasn't ever had a top-notch midfield enforcer, Montella has emphasized ball retention in the center by deploying three playmakers. This does allow Fiorentina to keep the ball easily, but it can also allow a more physical midfield to overpower the center and lead to counters (the Roma game). The additions of Badelj and Kurtic show that Montella recognizes this and wants more physicality in the midfield, although he clearly still wants technical players; don't expect to see any Gatussos or van Bommels.
The second major conclusion is that Montella doesn't place too much emphasis on natural width. Only the 4-3-3 (admittedly, his most common formation) requires four wide players. His willingness to sacrifice the center at the expense of the wings is something that most fans can probably recognize easily, since it results in two of the most enduring fan complaints. The first is that the attack tends to fizzle out around the opponents' box. This can be partially attributed to a lack of width high up the pitch: as Fiorentina move forward, the opponent can defend narrow, knowing that the wingbacks or fullbacks won't arrive until a solid defensive shape is set. Ceding the wide areas in defense is a good way to stop Fiorentina, especially when there isn't a target man wearing purple who can latch onto crosses. At the other end, Fiorentina tend to concede a lot of crosses. This is because the wingbacks or fullbacks often get overloaded by the opponents, which allows space to pick a cross. This also plays perfectly into the manual for beating Fiorentina: play on the break.
Another interesting point is that, despite having a three-man and four-man defense at his disposal, he doesn't deploy the former exclusively against teams with two strikers and the latter against teams with single strikers. Similarly, he doesn't switch to a three-man attack against a three-man defense or a two-man attack against a four-man defense. Most coaches who have both options will deploy them depending on the opponent's shape (Marcelo Bielsa and Pep Guardiola are notorious for this). His willingness to ignore the spare man at both ends shows that his strategy doesn't rely entirely on formations, but rather on putting individual players in positions to win individual battles. For example, he switched Cuadrado from the right to left to attack Roncaglia, whom he knew wouldn't be able to cope with the Colombian. Such a willingness to rely on players makes Montella seem more of a players' coach than a pure tactician, although his willingness to change or manipulate his team's shape shows a tactical nous not often associated with a pure players' coach.
The final trend I've noticed with Montella is a willingness to use players out of position. Early in his Fiorentina tenure, he experimented with Fernandez and Cuadrado as strikers, rather than switching to a single-striker system. Similarly, he's converted Alonso from a rampaging leftback to an assured left-sided centerback. Tomovic has received a lot of vitriol here for his tepid displays as a rightback, but he is, by trade, more of a centerback, and his struggles are more on Montella than him. Whether these positional switches are designed to take advantage of an opponent's weakness, to defend against an opponent's strength (unlikely, since Montella is not a reactive manager at all), or to put the eleven most on-form players on the pitch, or simply to be unpredictable, Montella's positional switches bear watching.
I'm skipping over a bunch of other shapes and trends that we've seen from Fiorentina under Montella in the interest of this is already a long article, and also because I can't think of any other big ones. Feel free to correct me in the comments.