Lots of good advice here. Might be good for a sticky actually.

The most important thing is that you talk to the passenger before-hand, as everyone here has mentioned. If you're trying to give instructions while under way, it won't work too well and you'll both be frustrated.

A couple of other things that haven't been mentioned yet. Be sure to use lots of back brake when slowing down. When riding by yourself, the front brake is usually enough 80% of the time. But with a passenger, you won't get as much weight transfer to the front and the front brake won't be as effective. You will be able to use the back brake pretty strongly, and will notice huge improvements in your stopping distance.

The other thing is a bit of a "soft" issue, as opposed to a "bike handling" issue. Keep your passenger's comfort in mind when riding. Don't tailgate, weave in traffic, or do dangerous stuff. Accelerate sensibly and try to brake well in advance of when you need to. Make it comfortable and fun. It's easy to scare a passenger to the point that they don't ever want to ride again. If you want to show them some speed and be a macho-man, pick your spots, in wide open places where there's no trouble. Pat them on the knee or give them the thumbs up to let them know you're cool and calm and everything's under control. This may pay dividends for you later, depending on your intentions.

And last thing - be careful. It's one thing to hurt yourself on a bike. Living with the responsibility for hurting a passenger who trusted you to be in control and return her home safely, is another thing entirely. If you go a bit slower, the ride lasts a bit longer, and that's good for all involved.

Have fun!

--- D