More pupils say to me that they are scared of roundabouts than any other traffic situation...but after a single lesson with me, no longer! The problem with roundabouts is that, by their very nature, there is likely to be lots of vehicles and lots happening at the same time. Trying to pick your way through that can be a bit daunting.
However, if you follow two basic principles, roundabouts become a lot easier. The first is to approach them with this thought in your mind: "Assume that I am going to go but be prepared to stop". This is in direct contradiction to normal junctions where the thought process tends to be "Assume I am going to stop but be prepared to go". The reason that a junction has been created as a roundabout is to keep traffic flowing so it is only sensible to approach it thinking in that way. Once you have that thought in your mind, the decision whether to go can be one of three things: Yes I can, in which case, go. No, I can't, in which case stop. Or Wait, I'm not sure yet... The first two of these are easy, the third is more difficult to judge. Ultimately, it will turn into a Yes or a No and for the learner it is more likely to be a No than a Yes, to be on the safe side. However, as you become more experienced you will find that judgement becomes easier.
The second principle is preparation with purpose. When you reach the roundabout you have already identified one thing that you have to do - to make a decision! In order to do that safely, you have to look. It is very easy to be preoccupied with mirrors, signals, speed, gear changes, braking etc. rather than looking so do them all before you get to the roundabout; that way you are free to do the most important thing which is looking at what is happening on the roundabout itself. Don't just look to the right. You need to look at your approach to the roundabout so that you stay in lane and don't hit the vehicle in front, a glance to the left just to make sure, looking at what is coming straight on and so on. Your head doesn't remain static - it moves constantly allowing you to make the correct assessment. Because you have already done all the preparation before getting to the roundabout you only have to look and decide.
Even with the correct approach sometimes it is difficult to make the correct judgement so this is what I do. Look for cars coming across your path. Three things will show their intentions. Their indicator, their road position and their speed. Base your judgement on all three. They may have left their indicator on by accident, they may have misjudged their position or speed but it is unlikely that they will have got all three wrong. If all three say to you that they are not coming round the roundabout, then the likelihood is that they are not so it is safe for you to proceed.
If the roundabout is busy, finding a gap can be even more problematic. Instructors talk about 'blocking vehicles' or some such similar phrase i.e., vehicles on the roundabout which interrupt traffic flow allowing you to get out. The most important thing is that a vehicle becomes blocking when other traffic stops for it, not when it is physically in the way. If you leave it too long, then the blocking vehicle itself may stop you from going. Anticipate vehicles not being in the way as well as being in the way.
Finally, remember that you are negotiating a roundabout, not an acrossabout so stick to your lane and don't cross lanes unnecessarily. If you do have to cross lanes, check in your mirrors (and possibly over your shoulder) before doing so that it is safe, indicating if appropriate.
I hope the above helps to make your passage round roundabouts a little smoother and safer.