Most of my work is done by hand and I use lots of different kinds of stitches, depending on what strikes my fancy at the time. I could probably spend a whole month on freestyle, explaining my process and the different kinds of stitches I use, but I'd rather show you some of what I've done. The one on the right is mainly in chain stitch. which is quick and easy and can cover a large area in a short amount of time.
The one above uses satin stitch. I was going for a Hungarian sort of design, which makes use of satin stitch quite a bit. The hardest part is making the edges of satin stitch look nice and if you do some sort of outline, that neatens things up pretty well.
This sashiko-inspired design is nothing more than running stitch with a few little French knots. The stitching itself is as easy as it gets, though the design can get pretty complicated.
This one uses a combination of several different kinds of stitches, including a double herringbone that was done so small that I realized that I either needed to either make bigger stitches or get some reading glasses. It makes my eyes hurt just thinking about it. To get the feathered effect, I mainly did feather stitches and cross stitches.
There are lots more, but those are enough to get you started. My go-to reference has always been The Reader's Digest Complete Guide to Needlework and if you don't have one, I highly recommend this one as essential to your needlework library.
Using a marking pen or pencil that washes out, you can free-draw whatever design pleases you and it doesn't have to be super complicated. Sometimes a simple design is all you need. Barring that, there are patterns that can be traced or ironed-on. Lately, I've taken to perusing the British Library's Flickr account. Those images are in the public domain and there are lots of interesting things that can be found there.
I've done a little in chain stitch and running stitch so far.
I could go on, but we'd be here forever. This is probably my favorite of the needle arts and one that's pretty easy to do if you start with a simple design and one or two basic stitches.