The montage action allows players to simulate the PCs' working toward a goal over time. The core rules speak to training, carousing, making preparations (reforging the magic sword, building the fortress, seeking out contacts), and performing intricate rituals, investigations, or meditations as examples of montages.
Montages are not defined as a mechanic unto themselves like the dungeon crawl or the journey action. Instead, the PCs identify a goal—training for the tournament; reforging the magic sword; finding the secret informant in a bar crawl—and then you choose a mechanic (or another downtime action) to allow that goal to be carried out. If you want to resolve the montage in a single scene, a three-act or single-act scene check might suffice. (Or if a single PC is involved, you can keep things simple and use a success check.)
Montage as a Scene Check
If you want to distribute a montage across multiple scenes, you can use the rules of social combat. If there is an NPC involved, you can base the TN for windows (i.e., the "social defense" in social combat) on a roll that makes sense for the montage. And if there isn't an NPC involved with the goal to set the TN, use an escalating TN starting at 11.
Let's look at two examples taking this approach.
In the first example, the PCs are searching for an informant who is said to possess incriminating evidence against the evil duke. The problem is that the informant is a notorious drunk who can only be found by carousing the local taverns.
In this second example, the PC is trying to reforge a sword, which ordinarily would take a great deal of time and effort on the PC's part that the table is not interested in playing in real time.
Montage Using Other Downtime Actions
When you montage, you can use the mechanics of other downtime actions to resolve windows of success. For example, if the montage involves the PCs traveling across the countryside to spread the word of the return of the Queen Who Lives, you might resolve each window of success as a monologue.
Similarly, if you are trying to simulate how the party's relationships deepen over time ahead of a harrowing battle that could mean their deaths, you might montage over the course of their travels where each window of success equates to a parley. In the parley, the PCs individually share their fears and doubts. The mechanical outcome here could be generating global story tags to use in the upcoming battle, for example.