LinkedIn allows you to join up to fifty groups, so there are plenty of chances for you to interact with the groups feature. A good starting point is to find local groups and branch out from there. Also, try to start with groups that are very relevant to your industry.
Like any relationship, your LinkedIn group relationships will grow over time as you develop connections. By connecting with others through LinkedIn groups, you will be able to grow your network of business professionals who might be potential clients of yours or may be able to help you grow your business. Join groups that are pertinent to your industry and company, so that you will be connecting with others who want to hear what you have to say and find value in what you bring to the table.
Choose your conversations wisely, and only contribute to group conversations where you have something valuable and useful to add. The main thing to remember about LinkedIn groups, like all other social networks, is to remain active so you will be able to develop relationships. If you take your time with LinkedIn groups, and treat each conversation as if it were a "real life" one (don't push your company on others, but offer helpful advice), you can develop real, meaningful connections with your other group members. They will learn that they can turn to you for answers and advice, and in turn, that they can trust your business. Answer questions, ask questions, and join in discussions where you can really add something to the conversation. Slowly but surely, you will be able to build relationships and in turn, build your business.