There are basic tools you need for the felt crafts I've created. Some of these are pattern specific (i.e. you don't need ribbon if you're not creating an ornament), but this will give you a basic idea of what you should have on hand to get started.
All of these are available at any craft store (JoAnn, Michael's), and you can also find a great many of these online on Amazon or the like. (Shopping w/no pants > regular shopping)
Ribbon:
I like to use thin ribbon for hanging ornaments. Offray works nicely, but any brand will do. This can be metallic, transparent (beware hot glue bleed-through for your fingers), etc.
Tape:
I love taping down my pattern pieces. I don't have to worry about wiggling and trying to hold the felt in place while making precision cuts. I like magic tape because it tears a bit more easily if you should happen to tape over a place where you are going to do stitch detailing. The non-matte tape also works but is harder to tear. For what it's worth...I use generic (Target brand, etc.) "invisible" tape a lot of the time.
Fabric Scissors:
You'll want a sharp fabric scissors with a nice point on it to cut out your felt pieces. Dull scissors will frustrate you because it will gnaw at the felt and make your edges all fuzzy and such. Which is why you'll also need...
Paper Scissors:
Did you ever use your mom's sewing scissors for paper? Did she threaten to cut you for real? Yeah. Don't do that. Have a separate paper scissors for cutting out paper pattern pieces.
OPTIONAL: Detail Fabric Scissors:
This is an optional piece--a fine-point fabric scissors. I find it useful for cutting out very small center detail. And (shhhhhh) I also use it for precision on the paper pattern. Do NOT tell my mom.
Glue Gun:
I glue a lot of the finer pieces together, and I also glue a lot of thread ends down. You're going to want a glue gun. You can use other glues (tacky glue works well for felt) but you're going to have to wait a long time in between gluing discrete pieces. And it gets all over.
Advantage hot glue gun: Near-instant gluing, precision tip, slight depth.
Disadvantage hot glue gun: Your fingertips. It burns. Plus strings of glue (that can be snipped later).
Here are my hot glue gun tips: Get the high temp ones (there are low temp and high temp versions). It will allow you more time for maneuverability on your project and the low temp will still burn your fingers, so you might as well go all in with high temp. Get one with a stand/rest that pivots out of the way for gluing time.
Don't fall asleep and leave your hot glue gun plugged in overnight. Ask me how I know.
Glue Sticks:
Get lots of these--you'll go through them faster than you think. There are two sizes--get the ones that match your glue gun (MOST hobby glue guns are mini size). Get clear ones. Get the ones that match your glue gun temp (when in doubt you can get the multi-temp ones--there are low temp, multi-temp, and high temp).
Embroidery Floss/Thread:
Hello embroidery thread! This is what embroidery thread looks like. It comes in these little skeins in almost any craft or fabric store. It is comprised of six little threads twisted together. This is important because while most felt craft just needs a 6-strand thread, sometimes you'll want to separate out 2-3 strands for some detail work.
Embroidery needles:
You'll want a good number of embroidery needles. I hate unthreading needles for the next color (I like to keep them threaded and stick them in a pincushion) so getting as many needles as you have thread colors is a good idea. I use finer needles (toward a 3 or 5) for detail work with 2-3 strands of thread. I use larger needles (16ish) for regular embroidery thread work. Get a variety pack and experiment with what works best for you--embroidery needles are fairly inexpensive.
Felt:
The base of your craft! Felt is available in individual sheets at craft stores. Most of the time this is all you need. It comes in myriad colors and is 25-50 cents a sheet. I keep a good stash around. If ordering online, this is 1.5mm (soft), not the 1mm (the 1mm is stiffer, so it can be really useful for letter detail, but it has a different look and isn't as accommodating for other things).
Felt also comes in bolts! So you can get a ton of a certain color (for busy book patterns, this is a necessity for the page bases).
Fine-Point Tweezers:
These, I love. Curved, fine-point tweezers are really, really good for holding small pieces while applying hot glue, and also having precision placement. They have saved many a fingertip of mine from being burned, or from me dropping an errant eye-piece onto someone's cheek. Plus? They're pretty cheap. I got a three-pack on Amazon for $6, and I like having multiple tweezers because there's always a use for them...and I lose them.
There you are! That will get you started with any basic felt pattern that I've created. (Oh, you'll also need a printer and paper...and a computer to process the PDF I suppose, and a power supply...and free time...but there's only so much I can help you with here.)