If you’re trying to build a relationship, ask questions. Most folks want to talk about things they are interested in–lots of folks enjoy talking about their lives.
Our default intuition is to talk about ourselves–sometimes to the point of dominating the conversation. Flip that upside down and work to keep the other person sharing. This requires tact–this is not an interrogation. Use warm body language and active listening; resist the urge to interrupt or share something that your new friend has reminded you of; think about good follow-up questions to keep the conversation going.
The counterintuitive effect is that your new friend will think that you are an interesting person–even if you’ve shared very little about your own life in the exchange.