Use the button on the dash to raise the headlights, remove the black plastic cover from around the headlight, unbolt the cover from the frame mechanism (IIRC).
See http://www.miata.net/garage/miata_radio_removal.html
I own a 1990 Miata, and since the Miata remained virtually unchanged from 1990-1997, it should be in the same place as mine. Open the hood, and toward the back left of the engine compartment there should be a plastic cover that will come up. Inside are the fuses.
Begin by removing the wiring harness from the back of your 1990 Ford Mustang headlight assembly. Remove the headlight assembly retaining bolts. Reverse the process to install your new headlight assembly.
On a 1991 Miata, the battery is in the trunk. It is probably the same on the 1990.
Here are step by step instructions and how to changer miata starter : http://www.racecaddy.com/mx5/tech/starter-mx5.html enjoy
There is a latch in the center console between the seats. Pull it, and it should open.
remove the panels in the boot across the back and you will se them behind there
If you look under the hood, behind the headlight panel, on the side towards the fender, you should see the motor that runs the headlight. There will probably be a cover on top of it. Remove the cover and you should see a knob that you can turn to move the headlight door. If the door wants to either open or close when you try to move it, just unplug the motor.
Set the headlights so that they both should be down. Open the hood, and find the fuses. Pull out the one that is for the headlights(Refer to Owner's Manual if you don't know which one it is). Now behind the headlight that is still up there is a post with a rubber cover. Pull off this cover, and there should be a red knob. This is how to hand crank the headlights. Turn this knob until the headlight is in the down position. Then replace the rubber cover, and the fuse. This is also a good way to free headlights that have frozen in place, if you live in a colder region. (I actually own a 1990, but since the Miata remained virtually unchanged from 1990 to 1997, this should still work.)
A 1990 300zx headlight is recessed into the bumper. To remove it, first loosen the headlight bracket bolts. Unplug the lights and push the housing outward. Be careful not to ruin the weather stripping for the lights.
The 1990 model of Miata came with a 1.6L DOHC engine and produced around 120 horsepower.
Put the headlights up, put up the engine lid, there are 4 screws on each headlight bucket, take them all off, remove the plastic buckets towards you, after removing there are a couple of screws holding the lights to the brackets, take those off and the light will come out, if you have stock head lamps you cant get the bulbs out, you must get new if damaged or burned.