This is my way. Call the 9 squares a grid and each individual box a box. All 9 grids call the whole.
Go through all numbers and use a pencil to write possibles in the corner of the box. Only put a possible in if it's one of two, no more or it gets confusing.[about as confusing as this answer I hear you say!] Often there will be two numbers only that fit same grid e.g. 3&7 this is one of the biggest helps as you can now eliminate those boxes as only 3&7 fit. This means that in the line 3&7 are in they can be eliminated as well.
I was going to put more of my ideas down but I've just had a look at the link jamspanner gave and it's much more succinct than mine! Go there.
Happy Sudokuing