Engine Electrical
The 2nd gen has a relatively robust charging system, but, with age, components can fail and are to be considered wear items. The following is a general troubleshooting and symptom diagnosis by component.
Battery
Batteries are a wear item, and will get weaker as time goes on. As far as recommendations, I haven't found a battery that I've been truly happy with that's priced reasonably and is easy to get. If you suspect the battery is getting weak, you can take it to an auto parts store like AutoZone and they'll do a free battery test and charge it up for you as well. To do a field test, look at the voltage across the terminals with a multimeter - it should be about 12.5 volts.
Make sure the battery is secured! Many cars I've worked on have had the battery sitting on the tray with no hold down - this can be dangerous! If you don't want to get the stock Mazda tiedown, very good ones can be had at most auto parts stores for a few bucks.
Always use battery terminal washers - they're small felt circles that are soaked with an anti-corrosive chemical. They're only 99 cents or so, and will prevent corrrosion. I've used them with the same terminals for 3-4 years now without the slightest hint of corrosion - they really work!
Battery Terminals
If your car has many miles on the clock, it's time to change those old terminals out. I HIGHLY recommend quick-release terminals. AutoZone carries terminals that have a lever and an adjusting knob on the side. Simply put the terminal on the battery with the lever up, tighten the knob, then push the lever into place - can't be simpler. To install them, you have to cut the old terminals off - I usually use a hacksaw or some good snips. Strip the wire about 1/2 inch from the end - the positive wire has 2 wires that you have to strip. The new terminal has a clamp that's held on with 2 bolts that clamps onto the wire. Clamp them on, reinstall, and you're good to go.
Main fuse box
This is on the driver's side shock tower. All of these fuses are available from any parts store, they're not special Mazda parts. If one blows, check to find out why it blew before replacing, and always replace with a fuse of the same rating, never higher or lower. The "main" fuse is different - it's bolted into the fuse block, unlike the others that simply pull out. To remove the main fuse, unbolt the fuse block and open the two "doors" on either side of the fuse block to reveal the bolts. Undo the bolts and remove. If you short hot power to ground while working on the car (like having a screwdriver touch the alternator's main terminal and ground), this fuse will blow.
Alternator
The 86-88 alternator is rated at 70 amps, and the '89-91 alternator is rated at about 80-85 amps. The life expectancy of the alternator is around 100-120,000 miles. If the headlights dim at idle, it's time to check the alternator. With a multimeter on the battery terminals with the car idling, no accessories on, you should see at least 13.5 volts, hopefully more. Below 13 volts and you have a problem. Turn the accessories on (AC, lights, stereo) and check the reading. If it's in the low 12v range, you may have a dying alternator. Check the voltage at the alternator's main terminal - if there is a difference in voltage with the alternator having more voltage than the positive terminal of the battery, it might be a good idea to run a heavy gauge wire from the main alternator terminal to the positive terminal of the battery. I have seen as much as a half volt drop between the two.
If the alternator is going, the best bet is a Mazda remanufactured alternator. Second is a Pep Boys alternator - some haven't had luck with them, but I've had quite good luck. You can also upgrade to the '89-91 alternator for more power. The only difference with the later alternator is the voltage regulator plug and the size of the ring terminal that goes on the main post of the alternator. More on this at a future date.
Starter
The starter seems to have similiar life expectancy of the alternator - about 100-120,000 miles. Sure sign the starter is going is slow cranking speed. If it is cranking slow, turn on the headlights - bright headlights are a dying starter, whereas dim headlights are a dying battery. Also, make sure the main connection to the starter is clean and in good shape.