Yes, steel siding can be painted. The steps involved depends on the condition of the siding. Most of the work is the preparation.
1) A good washing if the first step. This can be using a pressure washer or a garden hose depending on the situation. The idea is to remove the dust, dirt and paint oxidation. A mild soap can be used if the oxidation is severer. To help remove stubborn oxidation use a scrub brush or stiff push broom. Don't worry if some is still left behind.
2) Rust will need fixing. Use a automotive rust converter to neutralize any rust. Follow the instructions on the package. Holes can be filled with either a urethane caulking or repaired with Bondo.
The exact method depends on the repair and if there is a lot of flexibility to the siding. Bondo dries hard and pop off or crack if there is to much flexing. Spot prime the repaired areas with a universal oil based primer like Zinsser Cover Stain.
3) Steel siding should be primed before painting to insure a good bond. The same oil based primer used for repairs can be used on the rest of the siding. Or an acrylic primer can be used for the rest of the house.
4) Check the caulking around windows and doors. If there is silicone caulk, remove it. Use a high quality one part urethane. The caulking can be done before the hole house priming. Allow the urethane caulk to dry completely then prime with an oil based primer, same primer used for the repairs.
5) Mask and cover anything you don't want to paint.
Painting Steel Siding
Now you can paint. You can use a good 100% exterior acrylic paint. This type of paint has the flexibility needed and will hold up better than an oil base paint.
I like to spray steel siding, but you can brush and roll. Plan on two or more thin coats instead of one thick one. Thin coats of paint will look better.