How to get a key for the car trunk?

I have a non original key for a Honda civic ex 1999. It only works for the ignition and the driver door.

Is it possible to get another key that will open my passenger side door and my trunk? How long will it take and the price? Also who does it a locksmith?

That's a really tough situation there man.
That's why it is very important that you should always have your spare keys with you. So that in case you left your original one or lost it, then you can still open it.
In your first question, well it's really possible. Just ask from the manufacturing company of your car and just wait what they can help for you. I'm not sure about the pricing but I think there will be some considerations done when you try to deal with them.
When it comes to locksmiths, allservicemaster.com has all the kinds of locksmiths you need. I also lost my key before and tried to hire a locksmith from them and the results are really impressive.

The original keys were lost, or car was a repo. Door key and ignition key were from a junk car or purchased from dealer. This happens lot.
You need to re-pin the other two locks. You can open the lock cylinder and change the pins to fit your key.
Read this in detail to see how it works. Note sometimes it does not work, or you end up with a lock that any Honda key will open.
http://www.clubcivic.com/board/showthread.php?t=208118