Replace inside door handle drivers side - 2001 Mazda Tribute

SOURCE: Replace driver's side door hdle & locking mechanism on 02 Protege

Removing the door skins are not hard, the problem is that they normally use a special tool. Without the tool you may break a few of the plastic clips. If so no worries go to your local automotive department and look for the clips. 
You will also have at least one screw that attaches the skin to the door frame. Usually remove the bottom of door panel and work around both sides until you get to the window. Then remove the screw and unplug any of the power options..
Haynes or  Chiltion manual for your car should show you details.. It is easy for the average DIY person.
The handle is just as easy. Do you have metric and torx because you will need them.

SOURCE: Mazda 5 replacing external handle on sliding door

Your door should be held on with clips. Removing the panel is sometimes hard, just take a good WIDE flat head screwdriver, and whatever tool needed to remove the screws holding the panel on, and be careful. Check underneath the panel, by the inside handle, and the arm point for screws. Once removed, take your WIDE screw driver, and don't quite pry them off, more or less try to get it underneath and pull towards yourself. There is no real easy way, just try to be patient with it, and if you hit any binds, look for more screws, its just a matter of patience for sure.

SOURCE: driver side inside door handle replacement

I have the same problem and I can offer a temporary solution until you can get the handle replaced.

Remove the plastic handle guard. (It's simple- just open the screw cover and remove the screw.)

Push in on the rear of the triangular lock with your thumb and the door SHOULD open. At least it works for me.