Updated: Apr 15, 2022
To start blacksmithing or bladesmithing you'll need a few things.
Here's the bullet points without explanations.
Anvil and stand
Steel to forge. Start with a low alloy steel like 5160 or something like 1075 or 1085.
Here's the long winded version.
You need a heat source, the easiest setup that will allow you the most versatility initially is a single venturi burner forge. These run off propane.
Tongs (you'll need something to hold hot metal with). Realistically you can make tongs yourself. I highly recommend this because good tongs ain't cheap but mild steel is (relatively).
A hammer, a 2lb sledge will do the trick. It's important to smooth the face of the hammer and round the edges, otherwise it will make forging more difficult than it needs to be.
Some kind of anvil. Proper anvils are hardened and they are not cheap. However, as a beginner to find out if you even like blacksmithing/bladesmithing you can start with something inexpensive and eventually graduate to something better. My first anvil cost me 650... I bought it locally and while it worked well enough I would have been better served by buying a newer less expensive anvil. If I were to do it again I would buy a 70lb from Texas Farrier Supply or for even less money you can get something from Centaur Forge. The anvil is one of those tools that you can't make without other bigger tools. I know... I've tried. That being said, once you have these basics covered you can make many of the other tools you'll need to practice your craft. You will also need a stand of some sort. You can make one from 4x4 posts cut to the same height and bound together.
A grinder will be a necessity for knife making (an angle grinder can work in a pinch).
A slag bucket (holds water, used to cool tools and work that won't be hurt by a water quench.)
A quench tank used to quench work that requires a specific quenching medium (oil, water, super-quench). I used an ammo can for a long time. Your quench container should have a lid to put out fires.
Steel to forge. Start with a low alloy steel like 5160 or something like 1075 or 1085. You'll likely have to order these unless you have some leaf springs laying around.