This usage of "and" is quite common across the US (although long ago a friend who had lived all her life in Manhattan once told me she had never heard it and it made no sense, which I had trouble believing).
In speech, it is an exact synonym for "try to", and does not at all mean that one is doing two different things (trying and then succeeding) as many posters (and a literal reading) suggest.
Teylyn's point that this construction cannot be used in the past tense or in a question is a good one, in particular for showing that "and" is definitely not being used as a conjunction, but this may need refinement. In particular, I think it can sound acceptable in a question, as in #6:
1. He said he was gonna try an' fix his bike.
2. * Last I saw, he was tryin' an' fixin' his bike.
3. * Last I saw, he was tryin' an' fix his bike.
4. * I wonder if he tried 'n' fixed his bike?
5. * I wonder if he tried 'n' fix his bike?
6. Didja try an' fix your bike?
7. Well, try an' fix it!
8. * If he tries an' fix his bike, it'll only take a minute.
9. * If he tries an' fixes his bike, it'll only take a minute.
(starred ones sound wrong to me)
Since the infinitival "to" generally binds to the previous word rather than the following word (e.g. "gonna eat") (defying the latin-based grammar notion that "to" belongs to an indivisible unit, "the infinitive"), it seems that this use of "and" is similarly strongly tied to the verb "try", so "try and" is perhaps best thought of like "gonna" or "wanna". The inapplicability to third person singular (examples 8 and 9) reinforces the notion that it is a late-stage transformation based on final word form.
I'm not sure, but "try and" might also be semantically restricted as compared with "try to". "Try and" may imply that the activity of the following verb will be performed, but success is not guaranteed, while "try to" can also be used when the following verb is simply a goal or hope. On this theory, the following would not be ok (they sounded odd to me at first, but the more I repeat them to myself, the more ok they sound, so I'm not so sure about this anymore).
10. • He said he was gonna try an' get a promotion.
11. • He said he was gonna try an' get out early for good behavior.