Improving your position? A recommendation from IM Andrew Martin was to improve the position of your worst piece if you are not sure what move to make.  Are there any other ways one could improve their position besides the above recommendation?  I often find myself making useless moves, that mostly turn into blunders because I am not sure what to do in the position.  Sometimes this is a result of just thinking too hard and over-complicating things.

Here is a real-life sample that IM Andrew Martin used to express his point. In the 2007 British Championship between between Nicholas Pert (White) and Stewart Haslinger (Black), which can be found here, after 9. Re1, White showed what his plan was going to be and that was to play e4, which he did on move 10.  After 9...Be7 10. Re1, IM Andrew Martin says we reached a critical point in the game which Haslinger got wrong and that was to improve the position of his worst posted piece, which is his Knight on b8. Why? Because it is blocking his Rook on a8 and without the participation of the Rooks, black is not going to be in very good shape. White is going to dominate the center with e4 to e5. Instead of improving the position of the b8 Knight, Haslinger played 10...O-O. IM Andrew Martin instead suggests Black should have taken some pieces of e4 via:  10...Nxe4 11. Nxe4 dxe4 12. Bxe4 Bxe4 13. Rxe4 Nd7.  His reasoning was that, Black has now improved the position of his Knight, he is not as cramped as before, he can castle in peace, and White has no pawn breaks to upset the position.  Here is the complete game:

[FEN ""]
1. d4 d5 2. c4 c6 3. Nf3 Nf6 4. e3 a6 5. Nbd2 Bf5 6. Qb3 Qc7 7. Bd3 Bg6 8. O-O e6 9. Re1 Be7 10. e4 O-O 11. e5 Nfd7 12. Bxg6 hxg6 13. Nf1 Re8 14. Bg5 Bf8 15. Rac1 Qb6 16. Qc2 dxc4 17. Ne3 c5 18. d5 exd5 19. Nxd5 Qc6 20. Nf4 a5 21. e6 fxe6 22. Qxg6 Na6 23. Bd8 e5 24. Qxe8 Nc7 25. Qh5 exf4 26. Ng5
Improving your worst piece is indeed generally a great thing to do if it's not a bad idea for tactical reasons. Some other standard general ways to improve your position:


Develop all of your pieces.
Occupy an open file with a rook (or queen). Bonus: double or triple your pieces on this file.
If you already have occupied an open file with a rook, move it to your seventh rank if possible.
Put your rook opposite the enemy queen.
Connect your rooks (get the other pieces out of the way so they're defending each other).
Castle.
Make sure you can't get mated on the back rank.
Make sure you don't have any undefended pieces (even if they're not attacked).
Defend an important pawn or square more than once (known as overprotection).
In the endgame, centralize your king.


Of course, tactical opportunities (for you or your opponent) trump these considerations, but all of these are general principles for improving your position in such a way that tactical opportunities are likely to turn out in your favor in the future. For example, putting your rook opposite the opponent's queen means that he has to worry about some situations in which the pieces in between move.