This is a rough sketch of canvas (fabric, evenweave etc). The white squares represent the holes. To do a cross simple start from the back (leaving a strand to stitch down later) and bring the needle up on the bottom of the square you want to stitch. I usually start bottom right hand corner. The go to the top opposite side hole and bring your needle down to the back (in my case top left hand corner).
At this point you have done a half cross stitch. Fractional stitches ( 1/2 , 1/4 and 3/4 ) are often used.
Back to finishing the cross. Bring your needle to the other bottom corner come up and go down on the last hole - opposite top.
It is really important that you always go the same way, whether it's left to right or right to left - be consistent
The only hitch to this stitch (he he he a rhyme) is when you are doing squares going upwards. To go upwards do the first half stitch the same then go to the opposite TOP corner (not bottom). The effect on the front will look exactly the same, only the back will be slightly different.
You will base all your fractional stitches on this one stitch. You already know how to do a half stitch so next is the quarter stitch.
A quarter stitch is the same motion as a back stitch except it is only half the length so you will have to go down in the middle of the square where there is no definite hole.
A three quarter stitch is simple a half stitch and a quarter stitch.
In both quarter the three quarter stitches the chart will tell you which corner they should be in.
Fractional stitches are slightly easier on linen as you go "two over two" meaning that a square contains 9 holes not 4. There are extra holes between each "normal" hole and one in the middle (so you have a hole to use in the middle for the fractional stitches).
The other main stitch is a back stitch. These are done last and add detail and outlines to the design. Straight lines are pretty easy. Go up one hole, down the next, up the next hole and down the previous one.
You will have to improvise with curves, sometimes going through the fabric instead of the hole.
These are the basic stitches used however there is a myriad of speciality stitches. A lot are used in both embroidery and cross stitch. There are some great books out if you need help experimenting (with titles like A to Z of cross stitches etc), but most charts will contain information on how to do these stitches.