Find what to say in your favorite topics.
We all have things we are passionate about: activities, hobbies, projects, goals, ideas or jobs. Take some time to make a short but relevant list with the things you are most passionate about, and would make easy conversational topics for you.
Ask open ended questions.
One way to keep a conversation going is to get the other person talking. And the best way to do this is by addressing her open ended questions. These are questions which require more than simple 'yes' or 'no' answers, and offer the possibility of much richer answers.
Often, we find it hard to keep a conversation going not because we can't think of anything to say, but because we fear the other person won't enjoy that particular subject, fact or opinion we have in mind. However, most of time, this fear is not anchored in reality. Give it a try, and you'll discover that people are not that harsh and they can enjoy a lot of things in a conversation.
Let the other person end the silence.
Most people are uncomfortable with silences in a conversation. When one occurs, they immediately try to fill it by finding something to say. You can use this to keep a conversation going. When for example, you've just met a person at a party, you're talking and the conversation is stalling, do not leave that person and go find the peanuts or something like that. Instead, hang in there and let the silence work for you. Most of the time, the other person will eventually pick up the conversation and end the silence.