If you don't have a degree but do have the required coding skills you will get that job.

I have till date met 1000 programmers who have degrees from reputed institutes but don't know shit about coding.

@philbarr's method is actually very cool.

In the beginning you can work for start-ups and then switch.

Also: Take a look at this post Why can't programmers program?? by Jeff Atwood http://www.codinghorror.com/blog/2007/02/why-cant-programmer...