you need woven fabric that has even squares to stitch your x's into. i prefer to just use cross stitch cloth packaged for that purpose, because you can buy it based on how many stitches per inch you want. a pattern you follow will tell you which one to purchase (or you can draw your own designs on grid paper, too). i like 16 count the best- but it's totally your own preference. it's inexpensive and at every craft store. you also need a hoop.
there's only a couple rules to cross stitching correctly. one, you don't want to make knots on the back, it will make the finished product bumpy. instead leave a tail in the back when you first pull up the string and catch the tail with the first few stitches. and two, always do your stitches the same way. like, first, i always stitch from bottom left to top right and then i cross it the other way. it goes faster if you do all the bottom stitches then come back and cross them all.
always start in the center of your design and work out from there. literally count the squares and match them up to the pattern. where the pattern grid has a green x, you make a green x. it's that simple. work each color in its entirety, then the next and the next colors. be careful not to knot up your thread. you can usually pull little loopy knots out easily, but if you can't it is worth the time to get a new length of thread going. uniformity in x's is the key to a good looking design at the end.
when you are almost out of thread, or when you are done with a color, remember don't make knots, just slide the needle through some stitches in the back of the work and then cut off the extra. oh i almost forgot, embroidery thread comes in 6 string thickness. every pattern/ person has different preferences for the thickness they like to stitch the design with. i like a single strand. the correct way to separate the threads is to hold solid how many you want and slide all the rest down and off.
sometimes you use a backstitch to make skinny details or words. but really that's it. when you're done you can frame it, but i like to just glue the excess fabric back and keep it in the hoop. i love cross stitching, it is something you can do in bed with way less concentrating than knitting and is so portable. love it.
if you want to make this one, here's the pattern. as long as you start in the center of your canvas you can stitch this on any size canvas with any hoop and any colors. mine is in a 4" hoop with 16 count fabric.