Installing a new lock after you have removed the old one is fairly easy, unless you are Danny Smith apparently.

You have a couple of options.  First, you can follow the instructions that come with the lockset.  In the event you can't read detailed instructions in English, Spanish or French, please follow this idiots guide to installing a lockset.  This assumes that you have taken the old lock out and have a door with a hole in it.

1. Buy lockset.  Defiant and Kwikset are inexpensive and easy to drill out if the goober tenant leaves you in a lurch.
2. Remove from package.
3.  The first part to be installed is the bolt carrier.  It is long and thin and has a solid piece of steel inside a thin metal skin.  Push this through the small hole on the edge of the door.  This hole will be found on the side that DOES NOT have hinges on it.  There should be the word UP stamped on the frame.  The word UP goes at the top.  There are also two holes on the face stopper.  The stopper should be flush with the door and the holes will accept the two small, pointed, screws that are in the screw pack.
4. Depending of the location of the old lock in the door, the bolt carrier may need to be expanded.  This is done by simply unscrewing the carrier a half turn until it locks in place in the extended position.  You will know if you need to extend by inserting the carrier into the door edge and looking to see if the X or D looking hole in the carrier is in the middle of the large lock hole.
5. One this is inserted, you will take the lock face and insert it into the big hole that is on the front of the door.  There is a rod that will go through the X or D and come out the back of the door.  The tumbler face should be flush with the door. 
6. Take the knob and attach it to the tumbler face by inserting the rod that is now through the door into the hole on the back of the knob.
7. Line up the holes from the tumbler face, knob plate and bolt carrier.  Make sure the name of the lock (defiant, kwickset, etc.) is at the top of the tumbler face.  This will make it easier to line everything up.  On the knob, there may be a picture of a lock.  If so, this should also be at the top. 
8. Insert the long screws and tighten.
9. You should now be done.

If that doesn't get it done for you, then call a contractor or locksmith.  I would come and do it for you, Danny, but the flight to TX + my time would end up being an excessive expense.