I have a '99 SE and I do all the work on it myself. A great way to get to
know your vehicle is to purchase a copy of the Haynes Repair Manual $20
cdn. STUDY IT FROM FRONT TO BACK. It has great pictures and step by step
procedures. Section 5-13 tells you how to perform a starter motor and
circuit check. There is also a section on removal and installation for
both starter and solenoid. The starter/solenoid is bolted to the transaxle
bellhousing. Good Luck

Here's an old post I kept for reference, it may help. Orignal poster:
Daniel B Martin..

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You are reporting an intermittent no-crank problem.

Always do the easy check first.   If your vehicle is a 5-speed, make
sure
the clutch pedal is all the way down when you twist the key to START.
If
automatic, jiggle the shifter while attempting to crank.   Try
cranking in
both Park and Neutral.   If those steps are unsuccessful, consider ...

- discharged battery (dim headlights with engine off)
- weak battery (check voltage at terminals while cranking)
- loose or dirty battery terminal connections at the battery
- loose or dirty battery-to-body ground connection
- loose or dirty battery-to-engine block connection
- bad ignition switch
- bad clutch safety switch (5-speed)
- bad neutral safety switch (automatic)
- bad inhibitor relay
- bad solenoid
- bad starter
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Al Moodie.

I have a 97 SE that did the same thing and it turned out to be the ignition
switch.  An easy fix that cost around $50 for the part and 15 minutes of
time.