You have to go in the left-hand lane if you’re going to turn left off the roundabout (usually the first exit). You must signal for this. The only time you don’t signal is if you’re going “straight on”, which you also do by going in the left hand lane around the roundabout, then out. You would however signal left just before taking the appropriate exit, so everybody knows you’re leaving, including cars waiting ahead of you to enter the roundabout. You signal right to turn right, or to go right round the roundabout and back up the road you approached on. Turning right is the most difficult manoeuvre, because you must do it in the right-hand lane - which means crossing the left hand lane to exit. There shouldn’t be anyone there, really, but there can be.
I’m doing roundabouts in my driving lessons right now. They’re not my favourite.
Lots of big roundabouts have more than two lanes. They’re even more confusing. Many of the biggest are traffic-light controlled, which makes things much easier. But plenty are not.
There are also mini-roundabouts on minor roads, which are usually just there to stop traffic going at ridiculous speeds. You don’t have to be quite so careful with those to stick to the right lane - just not driving straight across the white circle in the middle is enough. Still, the same rules apply, technically.
I am told I should always do roundabouts in second gear. In third gear it should be more or less doable. Main thing is to take good early observations, because cars behind will often assume you’re going to go for it, and if you then slam on your brakes, you’ve had it. There entrance to a roundabout is a standard give-way once you’re stopped.
Oh, hey, I forgot about the best of all: double roundabouts.
There are only a few of these around, and - imho - nobody understands them, not even traffic cops. Not even the people who invented them. It’s basically two roundabouts, but as you leave one, instead of moving onto a new road you are immediately on the next roundabout, which you have to negotiate as before. It can get confusing because they’re usually just marked with paint, and you don’t know which paint to follow. Also you have to look right twice, and because all the cars are moving about in relative proximity to you anyway, you may find yourself accidentally giving way to cars that aren’t on the roundabout you’re on.
Hope that clears it all up for you. Buses in the UK are cheap and “reliable”. I say grab yourself a zonecard and stuff the stupid roundabouts.