You can get round graduated filters, that screw in just like most filters, but the problem is that they always have the split right in the middle. So the filter will sort of determine your composition, which doesn't sit well with me.
A better solution is to buy a square (rectangular) grad filter. This way, you can slide/position the filter to fit the composition that you want. To accommodate the square filters, there is usually a corresponding filter holder kit. A popular brand is Cokin. The holder is two pieces, one is the lens adapter, which has to match the filter diameter of the lens and the other part is the filter holder itself. Cokin has (I think) 3 sizes of filters. A, P and X(Pro). The smaller sizes are OK for smaller lenses and/or normal viewing angles, but if you have a really large lens or a really wide angle lens, you'll need a larger size.
Some people don't use holders at all, and just hold the filters up to the lens with their fingers.
As with all filters, there are cheap ones and expensive ones. You probably want to avoid the cheapest ones, but that being said, there should be plenty of old/used filters floating around because they are largely obsolete in the digital era.
I don't know the designations, but you may see that some filters have a greater ratio (darker on the dark side) and the transition from filter to clear will vary as well. For example, some might be a 'split' filter with a hard transition, while a 'grad' filter is more gradual.
There are also plenty of colors available (not just neutral).