When I opened the door the dome light comes on ,but when I start the truck it goes out,also the wipers work with the key switched on but go off when engine in started.
Wipers go on and off when driving . Problem just started ! When lights go out you can hear a relay click and again when they come on.

 

Describe your situation for each step (acc, off, on, start):

At each turn of the switch describe what is on and off (wipers, dome).

 

Key off dome lights work , key on ( but not started) dome lights and wipers( switched on ) work. When I start the engine the dome light goes out , wipers work and then they quit working ( the wipers start and stop .

 

the wipers could be the multi-function switch/lever. my old truck would randomly turn on the wipers while driving. I replaced the switch and all was well

 

Good chance it is your Combination/Turn Signal Switch,it's not very difficult to change it out,and Rockauto has one for $45.79(1998 FORD RANGER 2.5L L4 SOHC : Electrical-Switch & Relay : Wiper Switch-STANDARD MOTOR PRODUCTS Part # DS604T);They have a 5% discount code also:
RockAuto Parts Catalog
5% Discount Code: 423FA4590022
Expires: 01/02/2014
Be sure to enter the code in the ‘How Did You Hear about Us’ box to receive discount & enter ONLY the discount code, no other words or numbers. Please note that orders using discount codes must be placed online and the discount code must be entered before an order is submitted to receive the discount.

Here's a video to give you a heads-up on what's involved(level=EASY):

 

yeah, its called a multi-function switch.

 

I had to change mine out about a year ago. I broke it lol super easy to replace though.