Try one with different difficulty levels so you can get used to using different techniques, start with easy and move up once you want more of a challenge.
Using small numbers in the boxes is useful, but I try to save that for closer to the end otherwise it gets too confusing. I usually alternate between checking boxes, checking lines, and checking numbers.
So as for what this means, to check a box, I look for boxes which only have a few spaces left. I've attached a picture, so come back in a few mins if it has not attached yet. This is a good example (it came up when I googled free sudoku puzzles).
The centre right box here has three spaces, so it's a good one to start with. The missing numbers are 6, 7, 8.
The 8 cannot possibly go in either of the bottom two squares of this box because there is already an 8 in the bottom of the three centre rows. The only place it can go is in the empty square I have highlighted blue. So I would put the 8 in there.
That leaves two squares in this box and the numbers 6 and 7. 7 in the bottom-right box rules out the bottom-right square, so it has to go in the middle bottom square of this box. The other square must contain the 6. That box is now complete.
I would then move onto the bottom middle box, and the bottom right box. Anything I can't work out yet, I just leave blank.
Do pretty much the same for each row and column, again starting with those with the least number of spaces.
If I get stuck I move onto numbers. So for example, in this "easy" puzzle, the number 5 appears 6 times, so there are only 3x more 5s to place in this puzzle. The 3 rows which must contain a no. 5 are row 3, 6, and 8. The three columns that must contain a 5 are 2, 4, 5, and the three boxes are top middle, centre, and bottom left.
Row 8 it has to be between the 8 and 1, because the only other space is in box bottom centre, which already contains a 5. So I can place a 5 here between 8 and 1 in the bottom left box.
That means there are only 2x more 5s to place. The only possible places are row 3, column 4/5 or row 6, column 4/5.
Row 3, column 4 already has a number 2 in it so the 5 in row 3 must be in column 5.
Therefore the last 5 has to be row 6, column 4.
The more you fill in like this, the more boxes, rows, columns and numbers will get to a point where there are only 3 possible spaces (easy-ish) or even 2 spaces (very easy unless you get 2 which could be in either place - don't guess for this, but can use the small number technique). or 1 space (then the answer can only be one thing).
The fun comes when you make a mistake and then fill in more numbers based on the mistake - then you have to rub things out and it gets messy! But if you start with only gaps of 3/2/1 then you shouldn't make too many mistakes.