Positions with summer start dates will begin posting when people receive acceptances to graduate school, so you may start seeing them early in the spring or sooner. They start coming in droves after April 15.
I third the advice to get a two-year position if possible. When I started my current position, the PI advised me that they would support my applications to graduate school, as I had mentioned during my interview that I was in the middle of preparing to write applications. However, I had moved across the country for the position, and I would not have had enough experience in the three to four months I would have had on the job by application deadlines, so I postponed to the following cycle (this one). Overall, I would have had a better CV had I waited for another year with more publications, but I do not regret the decision to wait.
Resources that I have used:
Glassdoor
Indeed
Post-bacc RA Opportunities (spammers occasionally hit this site, but RA positions continue to be posted here from time to time)
Individual universities' career sites
What I did while searching was set job alerts and applied as soon as I received a notification. With Glassdoor and Indeed, those notifications may be delayed by a couple of days depending on how long it took for those sites to aggregate postings. For what it's worth, I've received interviews from applying using all of the above sources, but I seemed to get more success where there wasn't an HR screening process. For my current position, I had directly emailed the PI with a cover letter, CV, and writing sample in response to and as directed by a job posting. I had research interests that were relevant to the work that the lab was doing, which I was told was instrumental to my getting the job. However, I did simultaneously get an interview somewhere else (from which I withdrew when I took this job) for a position that was not related to my interests but to my previous experience, so it may be that you don't necessarily have to match the lab's interests if you have what they need.
Best of luck!