JOEL - When you say "barely know" I assume you are talking about someone you see at work or school, or perhaps a neighbor. First of all you need to do something to get you past the "fear of man" problem that causes most of us to not say anything. We are afraid of rejection or of what they might say or think of us. However, if you really have been prompted by the Spirit to talk to a particular person about the Gospel, then chances are they may be ready to hear about it. Otherwise why the prompting? Therefore no need to fear rejection.
If you are motivated by love and a desire to serve God, you will find ways to share the Gospel. A lot of what a person does will differ according to their own personality. Here are a few things you might consider in acting on the prompting:
Get to know the person better.
Start talking about anything to get lines of friendly communication going.
Mention something in your conversation that will prompt them to ask you a question. For example:
You: " I have this firiend who lived in South America for a couple of years"
They: "Oh really what was he doing there?"
You: "He was serving on a mission for our church"
They: "What church is that?"
ETC.
By just casually mentioning a few things that will identify you as a member of the Church, you will be able to tell by their response, facial expression, body language etc. whether or not they are interested in hearing more about it. If they seem interested, continue telling them about it. If not, continue to be their friend and wait for a more appropriate time. Most people will not be offended if you talk to them in a friendly, non-intimidating way about it. It's a good idea to always have a Church information pamphlet, magazine, or Book of Mormon handy to give them if they would like to read something about it. After you establish the fact that they would really like to know more, it is a good idea to suggest that they listen to what the missionaries have to say. It is always better if they start by learning some of the basics in a systematic teaching program rather than jumping from one subject to the next in an informal conversation. The full-time missionaries have been trained for this.