Before tackling the job head on there are few knowledge based tools you need to have, and in the world of mechanics patience is one of them

First, you or who ever is helping you do the work must have some understanding of the techniques involved by being able to make wire connections and read the schematics that will be used.
Second, you will need the tools such as a digital meter, test light, to verify that the correct connection is getting power to the proper circuit. As a first timer dealing with wires you may find it daunting or even a bit intimidating. This is especially the case when you try to untangle a bunch of wires dangling together not knowing which one goes where when you attempt making the right connection. If it doesn't go right the first time two things will happen. 1) You burn out something and then ask God for help. 2) Yell out some colorful expletive and then objects go flying. (not exactly in that order)
So to get started you will need to locate the wiring diagram of the car which you can find at :
AutoZone Auto Parts Stores | Motor Oil, Exhaust Systems, Suspension Parts, Car Starters, Car Stereo, Radiator Hoses, Headlights, Car Accessories, and More - AutoZone.com (sign up its free). There you will need to input all the information about your car to get the proper diagram. Once you got it, the next step is to have the proper tools to be able to remove the lower panels to get access to the wires. To do that look underneath the panels on the driver's side and find the fasteners to see what type of screwdrivers you need.
The next step is crucial, study the diagram to the best of your ability so you will be able to identify wires by their color code. For example: A typical wire will have R/LG written on the diagram. This means that the wire is Red with a Light Green stripe.
The next step is to know which color code wires were used and their respective locations on the car for the remote start system. Which you can find here:
'98 Ford Contour / Mercury Mystique Alarm / Remote Start Info.
Make a copy so you can have all the information with you when doing the work. When you have got everything you can start tearing into the panels.
Note: Before going into panic mode it will help you immensely by taking pictures of every step you do, so you can use it as reference when you are putting things together.
You ready ?