In general, the best uses of these groups are to connect with people in your target profession and/or working at one of your target employers, and to keep up-to-date with what is going on in your field or area of interest. You may also find posted job openings, identify potential job opportunities, and/or view discussions about a particular subject (like your industry or your profession).
Be very cautious about posting your resume in a group, even a group specifically for that purpose. Instead, be sure that your profile (like your LinkedIn Profile) is up-to-date, accurate, and looks "current." LinkedIn gives you this opportunity with status updates.
Marketing Yourself in a Group
Search through group listings to find groups focused on your industry or profession. There may not be jobs posted, but you can identify contacts and companies (as potential employers) which may prove just as useful.
Every group is different. Observe the postings to a group for a while (called "lurking") to see how people handle themselves and what is (and is NOT) acceptable. Then, as appropriate, add your relevant comments and posts, demonstrating your expertise in the area, your professionalism, and your maturity.