It's 95 degrees outside (37 Celsius) and the air conditioning fan in your 'Vous or 'Tec is going full tilt. Refreshingly cool air travels from the dashboard to your overheated frame. Halfway into your commute, the flow of cool air slows to a crawl. You feel the dashboard and yes, it's still cold, but the sound of air rushing is no longer there. You try turning off the recirculating air and are rewarded with a little better airflow, but it isn't quite enough. Worried about freezing the dashboard, you finally relent and shut of the air conditioning and open the windows. The blast of hot, humid air is anything but refreshing.
It looks like the resistor and possibly the blower have just quit on your ride. While you could take this in and spend $350 to get this done professionally (and I couldn't blame you), the idea of tackling this yourself and saving some money is tempting.
As always, you are responsible for your own work. This is a deceptively simple job that could take you a couple hours easily. There shouldn't be too many safety issues, but you're working on the dash next to a bomb that could literally explode in your face (read airbag). The blower is also very powerful and you could get scrapes and cuts from a moving fan. You'll also be playing with electricity, which even at 12 volts is enough to weld tools to the metal parts of the car and cause burns. You could damage other, more expensive parts of your ride or cause a fire. Use common sense (that thing so rare it should be a superpower) and do this at your own risk.
You'll need a 1/4 drive ratchet, universal joint and/or swivel sockets. A 5/16" or 8mm as well as a Phillip's or cross point screwdriver are mandatory as is a door pad tool. A jump box will help with testing the blower when you get it out and possibly save your electrical system. Unhook the battery if you want and it would be a good idea. I'm a bit on the crazy side, so I just made sure the key was off.
Remove the hush panel under the right side of the dash. This pries off with a door pad tool at the top and you can usually pull out the fasteners next to the carpet with your fingers or pliers. Remove the wire connection from the blower and three screws holding it to the heater assembly. Two are visible and one is toward the firewall. No sweat.
The resistor is where it gets interesting. This lives between the blower and the firewall and is held on with three screws. One is visible and the other two are right next to the dad-blamed firewall. Better pack your patience getting these loose as there is NO ROOM between the resistor and the firewall. You can remove the one screw and try wiggling the part out, but you risk breaking the heater box. Go ahead and get a swivel socket and loosen 'em up.
Honestly, I couldn't tell you the first thing about diagnosing the resistor itself. If the car has more than 100,000 miles and or the connector to the blower is melted, replace it.
The resistor is about $30 new, don't buy this part used as it's a wear item and will probably fail in short order. Who wants to do this again any time soon? Not me. The blower is $95 new, so a little more care needs to be taken before condemning it. Inspect the female end of the connector on the blower, if it's melted a bit you might be still be able to reuse it, but this is a gamble that it could fail real soon. If there isn't any obvious damage, you can use jumpers or cut the end off the old resistor and strip the wires. Put the blower in a vise and hook a wire to the jump box. If the blower spins, you you can save it. If not, replace the blower. If the connector is damaged at all, I'd bite the bullet and replace it. No sense in doing this job again. You can buy a used blower and expect to get a fair amount of use out of it. These are MUCH less expensive than at the auto parts store; I got mine for twenty and some change. Install everything in reverse order and tighten the screws snugly. Hook up the Molex connectors to the resistor and blower and before you button up the hush panel, hook up the battery and check your work. If the blower has all five speeds, you can finish up and relax. You have my permission. Maranatha!