How can I tell how many puffs are left in my albuterol inhaler?

That depends on the design of the inhaler. I am not familiar with albuterol, but I have used several different inhaled drugs and delivery systems over the past 30 years.

If the inhaler uses a pressurized canister to store and deliver the drug, there is no way to tell how much is left with any degree of accuracy. You need to keep count of how many doses you have used (N doses per day x M days in use) and ensure you have a replacement inhaler on hand before it runs out. You may be able to get a rough estimate on the amount remaining if you shake the canister and listen to it. If you can't hear anything moving inside the cannister or cannot feel any motion, it is probably almost empty.

If it is an inhaled-powder device, you can pry the top off with a thin-bladed screwdriver. There is a tube that runs down to the metering disk, the piece that rotates and measures the dosage when you rotate the base of the inhaler. The drug is inhaled up this tube, through the top of the inhaler, and into you lungs. If you rotate the base and do not see any powder in the holes or if there is little there, you will need to tap it on a surface and then click it two or three times to get a full dose. The inhaler is empty when there is too little powder to fill the metering holes.

When you replace the top, it will snap back on tightly; you can cut one or two of the locking tabs off so that the top can be popped off more easily. Although the inhaled-powder units usually have a level indicator, there is quite a bit more drug in the inhaler to guarantee the rated number of doses are available. Opening the top to check with allow you to extend, for example, a 200-dose inhaler to at least 225 doses and, maybe, up to 250 doses. This can save a fair bit of cash, as you don't need to refill it so often. The manufacturers redesigned the tops a few years ago to make their removal more difficult, but it can still be done without damaging the inhaler. (Thanks goes to my MD for showing me how to do this many years ago.)

Albuterol is very inexpensive, so you may want to just use it as directed and not try to get any extra out of it. You aren't guaranteed the full benefit once you go past the recommended limit.