The alternators fail in two basic ways.
Low output (no charge) and high output (high volts)
The Omega alternator, once removed, is easy to work on. Simply remove the the three cover securing screws on the rear.

This will reveal the diode pack (which VERY rarely fails on these models, large black metal assembly at the rear of the photo) and the brush/regulator pack (combined part, at front of photo, the regulator is the black item).

The two main casues of failure are a failed regualator (nomaly fails short and causes high output voltage) and low output. If the output is high then obtain a replacement brush/regulator pack and fit it. This is easily done by simply removing the two securing screws visable in the above picture.
If the ouput is low then try this first;
The connection from the brush/regultor module to 0V is via the securing screws, the positive supply is via a spring contact which can be seen here:

This picture clearly shows the problem, corrosion has set in and caused the contact to become poor, simply clean this up and refit, idealy this connection should be soldered to prevent future re-occurance.
Re-assemble an refit......and hopefuly an easy and very cheap fix!
Note: This some times shows early signs of failure by a slight flashing of the dash/MID lighting......
As an addition, the alternators used are easy to work on and noisey bearings are reasonably easy to replace using standard off the shelf parts.
The bearing sizes are as follows:
Front Bearing - 6303 2RS ID=17mm OD=47mm D=14mm
Rear Bearing - 6203 2RS ID=17mm OD=40mm D=12mm