There are several ways:
1. If you're in undergrad, tap into school resources. For example:
- E-mail professors who's research interests you and ask to work/volunteer with them
- Look into any research programs/internships that your school or other schools might offer (check with the science departments, pre-health advisors, career center, etc. at your school)
- See if your career center has some sort of alumni shadowing program set up. Shadow someone in research and see if you can work with them or if they know anyone looking willing to take you on. This might lead to a full-time job after graduation if you end up taking time between graduating and applying to d school.
2. If you're graduating, look on job posting forums and boards on the websites of your undergrad, and research hospitals and schools. Do this as soon as possible, so you can commit as close to 2 years of work as possible (Most labs want ~2 years, otherwise it's not worth it for them to train you. If you're a strong candidate and they are the type of lab that supports personal/career development and your dental school dreams, they will probably be ok with a little less). This method is kind of random, so it would be best to apply to as many as possible (don't stop until you get an actual offer). The reason it's more random is that some of those postings on research school/hospital websites are legit and they're really looking for someone, and sometimes it's a legal formality (they already have someone in mind to hire, but legally they have to make the position available to the public).
3. Finally, personal connections. From my experience being on the other side, labs are more likely to hire someone they have connections with even if it's a distant one just because having someone trustworthy vouch for a candidate gives the lab some degree of certainty that they're not hiring a crazy or completely incompetent person. If you don't personally know anyone in research, ask around/interact with as many different people as possible and you may get a lead. Even applying somewhere that has/had someone from your alma mater working there helps (assuming they left a good impression).
I've had two substantial research jobs, and I got them through methods 2 and 3 respectively. People in my previous lab have landed positions through all three methods.