Highlight your achievements at work with grace and respect for your peers and co-workers.
The quick and dirty tip is to find ways to help others that expose them to the good stuff you've done.
We all know the slimy sort of self-promoter. The ones who drip ... goo. "Hey," says Slime-boy, "Great day, isn't it? I just met my first quarter sales goals six weeks ahead of schedule and am trying to decide how to collect my bonus. A trip to Hawaii or a Caribbean cruise. What do you think?"
Here's what we think: "We think you're an arrogant jerk. We think you're trying to get ahead at our expense. We think you should take the cruise. That way, if your body is lost at sea, we won't have to attend the funeral."
Here's what we really think: We're jealous. We want that bonus, too! And we know what a moron Slime-boy is, and we do not like it when a moron out-produces us. Even worse, what if he's not a moron? What if he really is better than we are? We don't like people being better than we are. It means we have to work harder to keep up, or it might mean we're actually not capable of doing what they do. We don't like being not capable; that's what drives some people to torment math nerds in high school.
So, let's step back. All of those reactions are really one thing: self-promoting makes the promoter seem selfish, and invites listeners to feel inferior. If you want to self-promote, the best way I know is a paradox: do it in ways that help your listeners, and downplay your role. And please, don't be arrogant about it.
Try asking questions. If you ask your boss, "Is there anything I can help with, while I wait for the lab results to get back?" you offer help at the same time as telling your boss that you've sent your samples to the lab. "What can I do for you, now that the project has been sent to quality assurance?" says that your project is wrapped up and sent to quality assurance. In both cases, you're offering help, so rather than being "that guy," you're being that helpful guy.
(Note: "guy" is used for illustrative purposes only and should not be construed as an endorsement of any particular gender identity, sexual orientation, marital preference, or lack thereof.)