If you're pragmatic, you're practical. You're living in the real world, wearing comfortable shoes. If you're dogmatic, you follow the rules. You're living in the world you want, and acting a little stuck up about it.
Pragmatic people have their feet on the ground and their heads there, too. No time for dreaming! They're realistic. A pragmatic approach to something is the sensible one. A pragmatic way to fix a bike is to use the tools you have rather than the ones you wish you had. Examples:
"The academic and political atmosphere in the 1990s was decidedly pragmatic, rather than optimistic." (Guardian)
He had to make an effort to recover his usual state of mind, which was realistic and pragmatic. (The House of Spirits: A Novel)
"Shoes were thick-soled, while bags were pragmatic large backpacks." (Seattle Times)
Dogmatic people are very firm in their convictions which usually come from some authority. The authority is often religious, but it doesn't have to be. Anything dogmatic is by the book. If you're dogmatic, you're 100% sure of your system despite evidence to the contrary. Dogmatic can also mean close-minded. Check it out:
"We need more such balanced analyses, and fewer dogmatic opinions, on both sides." (Nature)
"When I became a cardiologist 30 years ago, I was pretty dogmatic about the low-fat, low-cholesterol diet to prevent heart disease." (Washington Post)
Pragmatic people know what time it is. Dogmatic people tell you what time it should be.