There are different hydraulic brake systems and they vary slightly in their bleeding procedure but the principle is broadly the same.
I am bleeding some Hope C2s on a friend's gnarly bike.
They are old but beautifully engineered and are closed system hydraulic brakes.
There are kits to make things easier but this is the old school way using a simple hose.
Step 1: Tools and consumables and naming parts.
A 26 mm spanner or an adjustable.
Some clean rags.
A small length of tubing or a bleed kit.
The correct brake fluid. ( Some use DOT some use mineral )
These pads are held in with two split pins; remove the pins and the pads just slide out.
Make sure that you do not touch the pad surface with your fingers as this will contaminate them.
Step 3: Taking the first step.undo this . . . .
The nipple on the brake caliper should be pointing upwards ( the rear one is already but the front one will need temporarily undoing by one bolt to allow it to be swiveled upwards.)
Adjust the brake lever clamp so that it is horizontal to the ground.
Put paper on the ground underneath the lever and brake to catch excess fluid.
Undo the large polygon nut ( master cylinder cap ) on the brake lever with a 26mm spanner.
Step 4: Setting up for bleeding.
Attach the tubing to the nipple and attach a container or rag to catch the fluid.
Put rag around this to catch drips.