How do i remove the right front out side door handle on a 1993 dodge dokota pick up truck?

No you don't need any special tool . Find all screws on out side of door trim panel and the window handle , the mirror cover plate , then just pull on edge of the panel .
Gently pry the front side door trim panel (3) from the front side door by disengaging the plastic retainers which secure the panel.
Position the door trim panel (3) away from the door in order to gain access to the front side window switch electrical connector, if equipped.
Disconnect the window switch electrical connector, if equipped.
Remove the door trim panel (3) from the vehicle.
Remove the front side window switch from the door trim panel (3) by releasing the 4 plastic retaining tabs, as needed.

Use a cloth in order to pull off the snap ring which secures the front side door window regulator handle (1), if equipped.
Remove the window regulator handle (1), if equipped.
Remove the front side master window switch, if equipped. Refer to Power Accessory Switch Panel Replacement .

Remove the front side door inside handle (1). Refer to Front Side Door Inside Handle Replacement .
Remove the outside rearview mirror opening cover (2).
Remove the screw which secures the front side door pull handle (4).

Front Side Door Inside Handle Replacement
Removal Procedure
Remove the screw which secures the front side door inside handle (1).
Slide the inside handle (1) forward in order to release the retaining tabs which secure the handle to the door.
Open the front side door inside handle rod retainer and remove the front side door inside handle rod from the inside handle (1).
Remove the inside handle (1) from the vehicle.

Check out youtube video showing how to do it !
How To Remove Install Front Door Panel Suzuki XL 7

Hi Roberta, here's the instructions on how to remove your door panel. I have to wonder though on why you are removing it, my guess is you window doesn't roll up or down and your replacing the regulator. Any way here goes.

REMOVAL

1. Remove the plug and remove screw attaching door pull cup to inner door panel.
2. Remove switch bezel and disconnect power window/memory switch.
3. Remove screws attaching trim panel to door from below map pocket.
4. If equipped, remove window crank. (Refer to 23 - BODY/DOOR - FRONT/WINDOW CRANK - REMOVAL)
5. Remove screw holding door trim to door panel from behind inside latch release handle .
6. Disengage clips attaching door trim to door frame around perimeter of panel.
7. Lift trim panel upward to disengage flange from inner belt molding at top of door.
8. Tilt top of trim panel away from door to gain access to latch linkage.
9. Disengage clip attaching linkage rod to inside latch release handle (INSIDE DOOR HANDLE LINKAGE).
10. Separate linkage rod from latch handle.
11. Disconnect the power door switch, courtesy lamp electrical connectors.
12. Remove front door trim panel from vehicle.

Hope this helps and have an awesome day Roberta!

Answer
FRONT DOOR TRIM PANEL
REMOVAL
Using a trim stick (available from parts stores), pry courtesy lamp from door trim.
Disconnect wire connector from courtesy lamp.
If equipped, remove screws attaching door assist handle to inner door panel.
If equipped, remove screw attaching door pull cup to inner door panel.
If equipped, remove screws attaching trim panel to door from below map pocket.
If equipped, remove window crank.
Using a trim stick, remove screw cover from switch panel.
Remove screws attaching switch panel to door trim.
Remove power accessary switch from door trim Front Door Switch Panel
Disconnect power switch from wire connector.
If equipped, using a small, flat bladed pry tool, remove memory seat/mirror switch and disconnect wire connector Memory Seat/Mirror Switch
If equipped, remove screw holding door trim to door panel from behind inside latch release handle.
Disengage clips attaching door trim to door frame around perimeter of panel Front Door Trim Panel
Lift trim panel upward to disengage flange from inner belt molding at top of door.
Tilt top of trim panel away from door to gain access to latch linkage.
Disengage clip attaching linkage rod to inside latch release handle Inside Door Handle Linkage
Separate linkage rod from latch handle.
Remove front door trim panel from vehicle.
INSTALLATION
Hold top of trim panel away from door to gain access to latch linkage.
Place linkage rod in position on latch handle.
Engage clip to hold linkage rod to inside latch release handle.
Place front door trim panel in position on door.
Install trim panel into inner belt molding at top of door.
Install clips to attach door trim to door frame around perimeter of panel.
If equipped, install screw to attach door trim to door panel behind inside latch release handle.
If equipped, connect power switch into wire connector.
Place power accessary switch in position on door trim.
Connect wire connector into memory seat/mirror switch and install switch into trim panel.
Install screws to attach accessary switch panel to door trim.
Install screw cover into switch panel.
If equipped, install window crank.
If equipped, install screws to attach trim panel to door inside map pocket.
If equipped, install screw to attach door pull cup to inner door panel.
If equipped, install screws to attach door assist handle to inner door panel.
Connect wire connector into courtesy lamp.
Install lamp in door trim.

take panel off back door from inside and release/open door

remove the door panel and peel back the plastic dust protection sheet then remove the door latch actuator rod at the door handle by pressing the plastic clip back to you and it will rotate to you and the rod will simply pull out of the handle then remove the two 10mm screws one on each side and the handle will come right out then just reverse procedure for installing the new one.It is actually a lot easier then it sounds,hope this helped

FRONT DOOR TRIM PANEL - REMOVAL
Release door latch and open door.
Roll window down.
Remove window crank Window Crank - Typical , if equipped.
Remove screws attaching trim panel to door Door Trim Panel and Trim Panel Screw
CAUTION: Do not forcibly pull trim panel from door, damage to trim panel may occur.

Simultaneously lift upward and outward to release retainer steps from inner door panel Trim Panel Retainer
Disengage inside handle linkage rod from inside handle.
Disconnect speaker harness wire connector Speaker And Power Mirror Connector
Disengage power mirror wire connector, if equipped (driver's side only) Speaker And Power Mirror Connector
Disengage clips attaching power window/lock switch panel to door trim panel. Disengage wire connector from switch panel, if equipped Power Door Lock/Window Connector
Separate door trim panel from vehicle.
INSTALLATION
Position trim panel at door.
Engage wire connector for window/lock switch panel, if equipped. Engage clips attaching power window/lock switch panel to door trim panel.
Engage power mirror wire connector, if equipped.
Connect speaker harness wire connector.
Engage inside handle linkage rod to inside handle.
Align trim panel retainer steps with inner door panel and slide trim panel into place.
Install screws attaching trim panel to door.
Install window crank, if equipped.

Hope helped with this; remember rated this help. Good luck.

You'll need to remove screws that are by the door handle, arm rest, under door and side of door and then gently pull back on the panel as there will also be retaining clips attached and you don't want to break them. You'll need to lift the door panel upwards in order to get it off the window ledge. If it's the inside handle, you'll need to disconnect the rod from the back of the handle. If it's the outside handle, you'll need to pull back the weather seal and use a socket wrench (10mm or 11mm I believe) and remove the mini bolts holding the outer handle on, be careful as I believe the lock cylinder is also held on by the same bolts. then you should be able to pop off the handle (disconnect the rod first)

if you hit the lock button a couple times, will it finally lock?

If so, then you will need to take door cover off and lube up the connectors as they probably got corroded.

There are five screws to be removed, two of which are Torx bit. One is in the center of the door panel towards the top. One is behind the door latch handle. One adjacent to the side view mirror, and two along the bottom. There is an access panel along side the door latch handle you need to pop off with a screw driver. It is triangular in shape and about 5 inches long. Once that is removed you will see the door latch linkage to latch handle. Disconnect the linkage by unsnapping the plastic retainer off of the linkag rod and swing it so the rod can be lifted out of the hole. The window crank handle is a *****, you will need a dentist's pick or similar to remove a retaining clip just behind the handle but in front of the panel. The it is just an upward and outward movement on the panel and it should come right out.

Got this idea from mpvclub.com: Get some stainless or aluminum sheet metal screws, drill pilot hole into the handle and into the receiving part behind, then screw in the screw. Do on both sides of handle (get appropriate length screw.) When done, get some putty or hardener to fill in the screw slot, let dry, then sand smooth, then paint with body color. Result is great and inexpensive.