How can I get a big of rust off my cast iron skillet?

Rub or spray with cooking oil /spray and place on hot burner. Allow to get very hot, remove and rub hard with paper towels or clean rag till no more rust comes off. Rinse with hot water and scrub with scrubber. Place back on hot burner till dry. Spray or rub with cooking oil and place in hot oven for approximately 30 mins. It is now clean, seasoned and ready for use.

Wire wool scouring pads

Remember that you never wash an iron skillet except when extremely dirty. Just wipe out with paper towels between uses. Each time you do wash it, re-season with oil and bake in oven for 30 minutes. Always heard it had to be burned before 1st use. Meaning put in a little oil and get it really hot til oil starts smoking, then let cool down.

http://www.hometalk.com/diy/clean/cast-iron-skillets/how-to-clean-rusty-cast-iron-pans-23562937

If steelwool fails use sandpaper. If that fails you've waited too long to save your skillet. Think of a interesting way to repurpose it...

Veg. Oil; let it sit to loosen the rust, then scrubb with a non-abrasive pad... then repeat/ Once the rust is removed you will have to season the pan all over again. It's easily done in the oven by coating with oil and heat for 30 min. at 35- degrees. After this use kosher salt to clean the pan and dry it briefly on the stovetop to remove any last traces of moisture.

If it's really rusted then you will need course steel wool or course scouring pads and a lot of work. Then oil it and heat it and never let it dry without oiling it again, I have rescued several

1st, never leave it in water! always wipe down with shortening after cleaning. Eventually you can clean it using only a paper towel. Mine are never touched with water as they are well seasoned using this method.

rub sand into it.

I can tell by the other suggestions that we are all confused as to what constitutes a "big of rust". In worst case I can imagine I would use a rotary wire brush in a drill motor to get the rust off/out. Then you can actually wash it with soap and water before seasoning it as suggested by several previous answers.

Sand the rust off using a plain steel wool pad with cooking oil

soak in vinegar, then with a little elbow action remove the remains. Then, neutralize the vinegar with baking soda. make sure to re season the skillet.

the vinegar and baking soda treatment works on all iron/carbon tools. (including shovels) it is just basic chemistry.

I was taught to use dry table salt. Just rub it and it is an abrasive to clean.