You should find a good book or books of dry fly patterns, there is a plethora to choose from. I love going to the bookstore and perusing fly books, when one jumps out at you buy it.
The Adams is probably the single most used generic dry mayfly pattern ever. The traditional tie is with a hackle collar of brown and grizzly, grizzly hackle tip wings - upright and divided, a medium gray body, and a tail of the same hackle fibers used in the collar. It is completely generic and works nearly everywhere. In various sizes it can be fished during most hatches of dark mayflies.
You will learn that the pretty much the only difference between a March Brown pattern and an Adams is the color of the components. This is true for every basic Catskill style dry fly. Sulphers? - use yellow dubbing and ginger hackle, PMD? - cream and gray, Blue winged olive? - olive and gray ... etc.
The most commonly used variation on the standard dry fly tie is called a "parachute." For this style fly you make a wing post out of a sturdier material that stands straight up then wind the hackle around that so it parallel to the body of the fly. This allows the fly to rest right on the water yet float, rather being propped up on the hackle tips.
Craven's fly box is an awesome site. I think the step by steps by Tightline Video
(on either youtube or vimeo) are some of the best anywhere.
Here is the standard Adams:
And Sulpher parachute just to clear up any confusion with what I've said.