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Here are a veiw videos that might help:

With a heavy bag:
Heavy Bag Drills Counter Punching From Blocks
Heavy Bag Drills Counterkicking
Heavy Bag Drills Leg Technique Training


With a focus mitts:
Counter Punching & Conditioning Drills


With a basketball:
The Basketball (Skip to about 5:35)

Here's a regimen that I've always found interesting and functional for developing the reflexes necessary to defend yourself effectively (and considerably lower budget than joining a defensive martial art). You can do it in the garage, a large room, or even outside.

Suspend two tennis balls from cords. Don't use thin strings, those won't hold up to the punishment you're going to be putting them through. You can buy tennis balls on cords at some stores (old folks use them in their garages to make certain they don't pull in too far.)

Stand in a fashion suitable to the martial art you intend to use to defend yourself. Set the balls swinging. Direction is irrelevant though I recommend starting them both moving in the same direction for simplicity's sake. Utilizing purely defensive maneuvers (to begin with) you can send the balls swinging in wilder and crazier directions and greater speed. Practice at leisure until you're sick of it, repeat. Eventually, you can throw in dodging maneuvers and counter-striking.

Keep your arms up, one close to you. Your chin inside, you don't want to be hit in the jaw. Don't give every hit your all, you'll miss sometime and it will have been wasted energy. Thats about all I can give.