I was there on Friday, my second time in a couple of years. You pick up your boarding ticket from a little shed on the harbour - it opened at 10.30 am for my noon sailing.
The boat has outside and inside seating. If you prefer to sit outside (like I do), make sure you're queuing up at the boat before they start boarding, they'll tell you when you get your ticket what time they start boarding. Each time I've been the boat has been full.
There's a little shop and a toilet on the boat, and there are toilets on the island too. The journey across takes about one hour.
When you get there, they'll do a short circuit of the island so you can see the seals and the seabirds on the cliffs. They repeat this circuit before returning back to Anstruther.
You'll be met on the island by a warden who'll give you an introduction to the island and guidance about where you can walk.
Arctic terns nest immediately around where the boat docks, so make sure you have a hat on, particularly if you end up on your own at some point as it makes you a bigger target!
When I was there, most people (about 100), took the right path up towards the visitor centre. This provided a good opportunity to head off on my own up the left path.
There are plenty of places where you can stop to sit and watch the birds as well as look down and see the seals swimming under the water.
They trap birds for ringing up near the main lighthouse - there are a few enclosed (inaccessible) gardens around the lighthouse and this is a good spot for the chance of seeing anything out of the ordinary, as well as common birds like chiffchaffs, so it's worth spending a little bit of time there.
There are several paths criss-crossing the island so you can easily get from one side to the other and even with 100 people there, you can find reasonable space to yourself. Be aware that seabirds nest right across the island including gulls which sometimes will be quite aggressive in defending their nests (although this was really only an issue at one point where the path takes you within a metre or two of a herring gull). The terns also aggressively defend the area around the visitor centre.
There's a RIB that goes across too, and while it gets to the island more quickly and potentially offers better, closer views of the water, it waits for the main boat to go in first, so in essence the people on this get the same time on the island as those on the main boat.