The actual physics of FTL are way beyond me, but I'm happy to share a users understanding.

Imagine another universe (or dimension, this explanation is wrong enough that it doesn't make a difference) where every point in this universe maps exactly to a point in the other universe (usually called otherspace unless you've trying to get a paper published in a really posh journal). That's useful because, although there's a one-to-one mapping between points here and points there, points that are next to each other here aren't next to each other there, and can be very far apart.

This is very useful for travel if:

1. You can get from here to otherspace
2. You can find a point in otherspace that maps to your destination (in, say, the next star system)
3. You can leave otherspace at the right point

A common theme of documentaries about the history of FTL is the great cost of time, effort, resources, lives, and rehabilitation of early travellers of solving the third of those problems, but these days even small ships can be fitted with enough of an FTL system to bounce from one well travelled system to the next.

As a more independent minded ship, my FTL systems are more complicated and better speced, but they operate much the same way:

1. Use the pulsar timing network to get a good position fix. (This is a normal background task anyway, but it's worth checking that the results make sense. I bent an antenna once and thought I was about to crash into a moon. That wasn't a great day)
2. Talk to the system location beacon to get updates about otherspace drift (did I mention that the points in otherspace move?)
3. Run route calculation based on the first two steps
4. Manouver very carefully to match the beacon's instructions.
5. Pour a bunch of energy into the holepunch (Yes, it's got a proper technical name, no, I'm not going to bother dredging it out of cold storage)
6. Flip the switch (metaphorically) and emerge into otherspace
7. Scan for, lock on to, and move towards the signal from the destination beacon. Depending on your start and end points, you might need to route through a few different beacons.
8. Arrive near your target beacon and again manouver to sit in the right place relative to the beacon.
9. Dump another pile of energy into the holepunch and flip the switch
10. Move away from the ingress point before another ship tries to punch out into the same space This one is paranoia and training, it's something that's drilled into ships (and pilots, I guess), but even at busy beacons there hasn't been a collision in living memory.
11. Wait for enough data from the pulsar timing network to accumulate to confirm you're in the right place
12. (Optional) Inform your crew/passengers/cargo that transfer was successful and they can resume duty/leave their seats/prepare for unloading

System to system travel time is dominated by travel time to/from beacons in realspace, and then by inter-beacon travel in otherspace. The flip from one to the other is effectively instantaneous.