So many people think they are such experts at human relations that the do not bother to think systematilly about their behavior in relationship to others.
In terms of relationships with coworkers, I would argue that actions speak louder than words. I think that the most important thing about building relationships with your coworkers is that they should see you as a team player. Not gossiping about them is part of it, but it is also important that you willingly help them when possible, even when you are not required to. It is important that you not try to take credit for everything and shift the blame to others. This is just as talking and listening.
Communication, both verbal and non-verbal play a big part in relationship building. It's a two way street of talking and listening. I would much rather talk to someone who is truly listening. When someone is listening, truly listening, they aren't just thinking of the next thing to say. They listen to what you say and give advice, gesture with a nod that they heard, ask a follow up question, or restate what the person said.
Another important aspect of communication is respect. To get respect people need to give respect. People will forget what you said, forget what you did, but never forget how you treated them. Treat others how you would like to be treated. Think about this when speaking to other people.
Strong relationships are also established through trust. If someone tells you a secret at work and you share this secret with others, they will not be able to trust you again. Office gossip makes people untrustworthy. People look at what others say and direct it towards themselves, i.e. if my co-worker is talking bad about someone behind their back, what are they saying about me?
When dealing with customers keep a personal boundary. Don't start talking about what you did on the weekend unless they ask. Even then, keep it simple. Don't go into too much detail or give personal information, i.e. I went out for supper with my husband, not we went out for supper at Applebee's and I had too many margaritas. This will make for an uncomfortable relationship between the client and company.