Can't speak for all schools, but NC State accepts bachelors into their Masters and PhD program. While getting your PhD, you have the option to earn an MS "en route".
> How does undergraduates find a research groups to join?
For larger, research-oriented schools, this is as easy as visiting each professor's website. Most will have a link to their current or archived projects and their recent publications. Similar to the joke that you can get any academic paper for free by emailing the professor, the same can happen with research. Ask them about it and if you can join in on any of the on-going projects.
For teaching-oriented schools, this can be a little more difficult. My bachelors program only had 1 (maybe 2) labs, so if that wasn't your interest good luck. You can still do the same process, find a professor in a research area you're interested in and speak to them. There may not be funding, but you could be the spark under that prof's butt to start applying for some grants.
There are 8 or 9 former classmates of mine with PhDs and only one went out of his way to get a Master's prior, and only because it was a much more prestigious institution (Georgetown) than our undergrad (unknown liberal arts college). Everyone else either entered their respective programs directly from undergrad or had industry/life experience first.
At least at most US schools, you do not. Having one helps your chances of being accepted in most cases though
> How does undergraduates find a research groups to join?
Research fairs like career fairs, or just asking profs from classes you enjoyed - every undergrad I knew in grad school just asked my prof if they could try out research.
Don't you need a master's degree to be eligible for a doctorate program?
> If you're an undergraduate and harbor the slightest ambition to get a PhD, drop what you're doing right now and start looking for a research group to join.
How does undergraduates find a research groups to join?