How do you change out front struts on a 1998 ford contour?

You need to obtain a repair manual.
Your local auto parts retailer should have a Haynes manual for this car.

Verbal descriptions from well-meaning forum members–without illustrations–will not suffice if you want to do it correctly–the first time.

In addition to VDC’s good advice, realize you’ll have to do the (pretty dangerous) operation of compressing the springs, unless you buy a spring/strut pre-assembled. I don’t like to do it. This is one case where it might make more sense to have a pro do the strut replacement.

Take it to a front end shop and have them do it. Believe me, this job is not for the average, or even above average, shadetree mechanic. Many times on these cars, you have to lower the subframe slightly to get the struts to come out of the steering knuckle. Sometimes a five foot pry bar will get them out. I did one several years ago and it was memorable.

That’s why I despise that sort of strut design - my Taurus you either drop the subframe slightly or: disconnect tie rod, disconnect ball joint, remove brakes, pull axle from hub. THEN you can disconnect the sway bar link and “easily” get the strut out. Ridiculous. My Camry with its two pinch bolts that hold the strut to a flange on the knuckle (rather than the strut sitting in a pocket) is MUCH easier to swap struts on. And believe me, I have plenty of experience on that car. 45 minutes per side, even if I have to cut the sway bar link off with a hacksaw.

I’m with you - I truly do not like the idea of spring compressors.

However, I do wonder if anyone has tried one of these:

That seems FAR, FAR safer, since the two sides of the compressor are held together and cannot slide relative to each other. Naturally, the one review shows a weakness of many Harbor Freight tools - lack of longevity… but the concept seems MUCH better to me.