I have done it. You have to call a organization and tell them what you want to donate. If they do a phone accept, then they will make arrangements to get it. You must have title to car, and be ready for them. Be sure you get a receipt. I also would take pictures of person towing car away with picture of condition. Also print out the KBB value from online before they take it so if IRS calls you in to prove the value, you can. You only get what value what charity sells the car for.
If you take the standard itemization on 1040, then its not worth your time to donate the car. If you do the long version and have enough itemized deductions to put on your taxes, remember - you are NOT taking a full dollars off from exact taxes you owe. Lets say the car is worth 1000 bucks according to KBB value and you do it on taxes, then you might see 100 off from your taxes.
If you are on disability income - and you are healthy, single, I dont see the point donating your car. It's not a money saving thing you can do. If you are married, with a mortgage, kids, maybe with medical expenses, then it makes sense to donate if you need to get rid of a car and it goes to your favorite charity. Otherwise.... forget it.