What follows below is a number of ideas for your own study in no particular order. Remember not to get fixated on any one, and to choose something that you find enjoyable and useful.
If you're a beginner then you should visit the tips produced for the UK Go Challenge? They're not just tips, but include problems and answers, and you'll probably get something out them if you go through them a second time! When you've finished them go back to our main Getting Better page, rather than reading the rest of this page below...
This does NOT NOT NOT mean learning sequences of moves. You can get to shodan quite happily knowing no joseki at all, but the moves that you play will turn out to do the same sort of jobs.
Josekis are just moves that are often played by good players, but only in the right context. So look at the result of a strong players exchange in the context of the whole board. Then use that to calibrate your judgement. That much territory is worth that much influence, that much aji, etc. Josekis are a good source of tesuji and good shape examples, but it requires careful thought to pick them out.
Remember that many moves in a joseki will be "pro-only" ones - they only just work, and should only be played if you really know the right sequence to live/kill a group. Much better to play a move you yourself can prove works. It's also always a good exercise to look closely at moves that you find unexpected. Try to find the nasty replies to the move that you would have played.
Lastly, notice the points at which pros find it reasonable to tenuki, and leave something unplayed. That way, you can put off difficult decisions and only come back to a situation when it's easier to tell in which direction you want to play.
This does NOT mean just reading the comments! Ideally, you should actually put the stones out physically on a board, as this will give you time to consider the next move properly, with no distractions.Think about the balance of strong and weak groups, and try to upgrade your judgement.
Always be on the lookout for good shape to emulate, but be careful - pros will sometimes play moves that only work in the particular board situation they are in because of a seemingly distant stone. Ladders are just the simplest case of this sort of thing. Also note the best invasion points of common structures. Don't bother going too far into the game either - it becomes harder to gleen useful general knowledge.
Find someone that you would normally play on a few stones, and ask them for an even teaching game. You should expect to get advice and explanation /after/ you play your moves, and you decide together what move to accept and proceed in the game with. You may want to finish the game, or you may not, and ask your teacher what they want - remember that you are being given a favour. Hopefully, they will enjoy pontificating though!
Try to choose problems that are at the right level. This means ones that are actually pretty easy for you, solvable in 30 seconds or so. Remember though that solving a problem doesn't mean guessing the right move. It means proving the right move to a level of certainty such that you could play it in a game.
There's a life and death problem website to visit called GoProblems.Com. It starts off easy, but will trouble the best of our players with the most difficult problems...
First get a record of your game. Online this is easy, for other games see here. Don't take it too far into the game. Then, you should first look at the record yourself, and put in your own comments about what you think is going on. This will make the job of the person commenting much easier - they won't waste time on things you understand, thay can go directly to things where you are mistaken or missing something important.
Don't worry about knowing the correct sequences - you can work those out during a game. The thing to know is that a given shape is dead, or alive, or unsettled, so that you can shortcut your reading at that point.
Consider analysing a game with your opponent immediately afterwards. You don't need to go too far in, but talk about the turning points. Try to find the places where your opinion differs from your oponent. Those are interesting, and worth asking a stronger player about. Also, were there any life and death fights? Try to work out what move was the last one that might have changed the result in the game.
Consider experimenting with changing your style of play. If you normally play for territory, try to play for thickness, or vice-versa.
Try to be very conscious of the nature of each one of your moves, what its aims and objectives are. If you are playing a move that you want to do something (like be connected), then make sure that it actually really does defintely work, with a little extra reading. If it later turns out not to work, then you have learned something! If a group that you thought safe dies, then you 've learned something. If you were attacking a group, and your opponent ignores it and it's not a severe attack, then the original move was faulty - you've learned something.