How do you get rid of rust on cast iron?
My griddle has rust on various places and a pan has a couple small rust patches on the inside walls

Abrasion

A good coat of seasoning. Best done by stripping to bare metal then building up of several thin coats.

If not stripping and the rust is just surface flash rust you can give it a good scrub under HOT water with copper or stainless scrub pads then dry it well by tucking in a hot oven. Once the metal is hot to the touch rub on a thin coat of your favorite seasoning oil. I prefer flaxseed oil. Tuck back into the hot oven for an hour then let it slowly come back to room temp in the oven. Multiple thin layers best.

Deep rust and pitting needs a full strip and possibly electrolysis to get down to bare clean iron.

If you're only doing the one piece (or just a few) the easiest way is soaking the pan in a 50/50 solution of white vinegar and water. Let it soak for a few hours then scrub it with a stainless steel scouring pad - I don't recommend using a copper scrubbie as it will transfer small amounts of the copper to the iron and will give a brassy look. Once I get the rust off I wash the pan using hot water and Dawn dish soap to remove the residue and then give a second scrub with Barkeeper's Friend or Comet cleanser and the stainless scrubbie. When you've got the surface clean rinse with COLD water - rinsing with hot water will induce flash rusting. Wipe the piece dry with a wad of paper towel - you will likely still get some black residue, but that's normal. Season it once it's completely dry or later - I've kept unseasoned pans cleaned this way rust-free for years. I've been a cast iron cookware collector and seller for a number of years and do all the cleaning and seasoning in batches.

vinegar will get it off. buy the cheapest gallons you can find. put the pan in a plastic tote and submerge it. after two or three day rinse it off under cold water. if there is still rust repeat with fresh vinegar. if its just light rust use steel wool and running water. the orange color still there is no big deal. just season rust and all after you scrub and rinse it good. wipe the water out with towels and then dry on a stove burner before applying whatever you like to season with

Awesome thanks everyone. I think it's just light surface rust. I'll give it a go this week

The old way was to build a good wood fire and develop a deep bed of coals, then bury the pan in the coals and keep it there til the coals are cold,. you should have bare clean iron then.