Lifehacker provides some nice tips on editing your own work.
As any writer or editor will tell you, critiquing someone else's work is much easier than deconstructing your own, because outside eyes bring a fresh perspective. To approach your own work critically, you need to simulate this "outsider" perspective by viewing it in a form other than the one you wrote it in.
If you typed it, print it out. Give it a quick read-through, then wield your red pen and start slashing.
There are some other great tips as well, but I'd also add two more.
1. Always read your piece from the bottom up. This forces you to read the paragraphs independently. The biggest problem with editing your own work is reading what you actually wrote instead of what you thought you wrote.
2. Along with checking adjectives and adverbs as Lifehacker suggests, I'd add check pronouns. Confusing pronoun use can really kill the meaning of a sentence.