You don’t have to spend a lot of money to get your students (or yourself) equipped to adjust reeds. This is not a post on how to adjust reeds, rather it’s a list of the specific things to collect so the adjustments can happen. The following is a list of the materials I recommend and the order I recommend getting them. I’ve written this as if I were talking to a student so you can email them the link to this post and save yourself the trouble of writing it yourself!
The First Things to Get
To get started as a reed adjuster, you really only need two things: pliers and sandpaper.
Pliers: Any old set of pliers will get the job done. Go out to the tool shed and poke around. You can probably find something that will work. If you are willing to invest $8–30, then head to the hardware store (or Amazon) and look for a pair of lineman’s pliers. Lineman’s pliers have a blunt end. It’s easier to grasp wires with a blunt end than it is with needlenose pliers. I like the 5–6 inch long ones because they fit well in my bassoon case.
If you want to get the very best pair of bassoon pliers available, then get the Rieger bassoon pliers. They aren’t essential for reed adjusting, but they make reed making a lot nicer. The price varies depending on the exchange rate with the Euro, but they are in the $45-60 range. (Get them from Forrests, Hodge, Miller Marketing, Bob Williams, etc.)
Sandpaper: Sandpaper is infinitely useful when working on reeds. The two main things to remember are that it needs to be wet/dry sandpaper and the grit needs to be in the 400-800 range. Grit less than 400 can shred your reed, and grit above 800 takes forever to see results. This is the stuff I’m talking about: 
The Second Group of Items to Get
When I go to a rehearsal or a performance, I like to have three more things in addition to my pliers and sandpaper: a holding mandrel, a plaque, and a nice file. With these five items, I can make 95% of the adjustments that come up.
Holding Mandrel: You need one of these if you plan to take cane off your reed. You put the bocal end of the reed on it and it stabilizes the reed and makes it easier to hold as you work on it. You use a mandrel when you use a knife or a file (or sometimes sandpaper). There are lots of mandrels available. You don’t need a fancy holding mandrel. I recommend the regular Fox holding mandrel.
Plaque: This is what you place between the blades so you can work with a knife or file. You can buy one on Amazon, but I recommend buying a few from an online double reed shop. The black plastic and clear plastic ones are my favorites. They make it easy to see the thick vs. thin parts of your reed. And they are only $2 each. I hate the metal ones. They are heavy, can dull your knife, and cost too much. Don’t even bother with the lighted plaques.
File: For on-the-go reed adjusting, files are far superior to knives. Files are allowed in schools, allowed on airplanes, don’t need to be sharped, and are easier to use! Even if you (or your teacher) are die-hard knife users, I urge you to get a quality file and learn how to use it. I recommend a triangular diamond file. I’ve had mine for 15+ years and it’s still as good as new. I’ve ordered cheap file sets from double reed companies. They rusted and didn’t work very well. I tell my students to use a really cheap metal nail file from the drugstore until they save up enough to buy a good diamond file. If you choose this route, make sure the nail file is gritty (not the kind with lines) and make sure it’s metal! Cardboard emery boards fall apart in water.
Most of these items need to be ordered from a double reed shop.
Brass Wire: Make sure you get 22 gauge round soft brass wire. The word soft is important. (Some teachers like 21 gauge and others like 23 gauge. Check with your teacher.)
Duco Cement: This is reed glue that you can use to glue the wrapping of your store-bought bassoon reed back on. Because let’s be honest–they always fall off. You can also use nail polish in a pinch.
The following items are expensive, but they are really useful.
Dial Indicator: These are used to measure the thickness of your reed. Using one allows you to get really scientific with your reed adjusting/making. Expect to pay $100-300.
Tip Clipper: These come in handy when the reed you bought/made is flat in pitch. If you plan to make a lot of reeds, you will definitely want to invest in one of these. My favorite brand is Rieger. They run $175-250.
Reamer: You use one of these when your reed doesn’t fit on your bocal. There are two kinds—the spiral reamer and the diamond reamer. The spiral reamer works more quickly. Both are useful. Again, Rieger is my favorite brand, but Bob Williams has some nice ones, as do other double reed shops. Plan on $75-100 each.