My Husband and I would like to redo and organize our garage at the lowest expense we can. We need to "strip" the floor of oil, greese, etc. off the floor and then we were wanting to paint it. We have never done anything like this and need some direction please.

Epoxy paint is the way to go. Do a search. See what prep they prefer.

Pressure washing is a standard way of removing the dirt.

Any concrete that's painted usually needs to be etched in muratic acid.

I have done this a few times. Prep is 95% of the job. If you do not prep right, the epoxy will not stick. First, I use a torch to burn the oil out of the concrete. One of those weed burner torches that hooks to a small propane bottle. Heat the oil till it starts smoking then back off. You don't want to get it so hot as to pop the concrete. Keep heating the oil till it stops smoking. It will be, for the most part evaporated. When that is done, pressure wash the whole floor with no less than 3000psi. Use a tight tip and do every square inch.
Next, get a few gallons of Muratic acid from home depot. Mix one gallon of Acid with two gallons of water in a 5 gallon bucket. Pour it on the floor and spread it around with a good stiff push broom, working it in as you go. VERY IMPORTANT! USE A BIG FAN, DO NOT BREATH VAPOR AND OPEN EVERY DOOR FOR GOOD VENTALATION!
This will etch the concrete by removing a little of the smooth finish, exposing the fine aggregate. When the acid has done its job, you must neutralize it with vineger or it will keep working. When this is done, rinse extremely well.
Next, let dry completely. Use heater and fan. It cannot be too dry. If it is even just a little bit moist, the paint will peel.
When completely dry, tape off and apply epoxy as per directions.
It is a lot of work but if you do not prep properly, you might as well not even paint it.

Missed the torch. For that amount of area, an acid gas respirator seems to be in order. Full face is probably best because of the eyes.

Yes, that is what I use. I tried to acid etch a basement floor a while back. Take my advice, don't ever do that! Even with the mask it got way to narley!