I think if you know early on that grad school is something you might want to do, it's not too hard. I started working as an undergrad RA my sophomore year by approaching one of my professors in the spring quarter of my freshman year and asking if there was anything I could do to help out. I basically helped a more senior undergrad with his honors thesis -- I helped run subjects, review papers, collect data in the field, etc. The next year I became co-Lab Manager (I graduated after that year). Many other undergrads did similar work in that lab, and in fact, most of us went on to good grad programs, probably partially on the strength of strong recommendations.
During my second year, I also approached another professor in the dept who was a MacArthur Fellow and asked the same thing, and ended up helping him transcribe and code a bunch of interviews he had done. Wasn't the sexiest work I've ever done, but voila, at the end of three years, I had one very strong letter of rec from one professor (well published), who also reached out through his network to put in a good word for me at CMU, and another rec from a professor who was a MacArthur Fellow.
Granted, I think something that's really cool about my undergrad (UCSD) and department (Cognitive Science) is that they are very open to undergrads helping out in research capacities, but it doesn't seem like something that is out of the reach of most self starting undergrads.