If fence generally okay, you will need a pinch bar (long straight heavy metal spike) posts post knocker, hammer and wire fencing staples.
Ignore old posts don't bother removing them it's a pain in the butt.
Use pinch bar to start a new post position about a foot from the broken post. Usually you just jab into the ground and wiggle it a lot to make a hole. Repeat till spike goes in at least a ft maybe more... Stand new post in spiked hole, use post knocker to drive in, this is hard work, and is easier with 2 people... Beware the post knocker will get snagged on fencing unless you push it out of the way temporarily, drive post in as far as necessary, or till it really won't go any further, should be at least 18inches in the ground.
Staple fence to post copying existing posts, not normally stapled tight as wires need to move when tightened.
If all that all fails get a friend to demonstrate first as it's a lot easier to do than type out...