For collars and cuffs, or sizing silk, I will occasionally break out the spray starch (aerosol bottle found the laundry aisle of your favorite store), but--as it's meant for tidying up modern men's shirts, etc.--the instant stuff just doesn't keep a petticoat in shape. For these, I use a heftier cornstarch mixture, adapted from the recipes found here.
Unfortunately, living in a small apartment means no private laundry room and no spacious yard with a clotheslines from which to drip-dry petticoats. What I do have: a stove, bathtub, and clothes hangers. A clean bucket/basin (I use a plastic garbage can otherwise designed for clean recyclables) also helps with the petticoats. In a pinch, a clean sink could be used. If you have roommates, butter them up, or wait until they're gone for a weekend.
First up, dissolve about a quarter of cup of corn starch in 2 cups of water, adding water to a total of 4 cups (this will get 2 plain petticoats and whatever accessories; doubled, using the largest saucepan I have, it'll take care of the my corded petticoat as well). Place on medium heat, stirring occasionally, until it boils. When the entire thing has the appearance and consistency of pale snot, after about 1 min of boiling, it's ready to use.
Next fill the bucket/basin/garbage can with 4-ish cups of cold water, dump in the starch mixture, and submerge the first petticoat. Mind the boiling starch mixture is HOT, and take care with your hands; let it cool a bit before using if necessary. When the first petticoat is thoroughly soaked, wring it out over the basin, and hang over the tub using a clothes hanger.
Continue with the rest of the petticoats, wringing them out above the basin--else, you'll run out of starch very quickly. I usually run my sunbonnet full-strength (if there's enough starch left), then dilute it with more water before dipping aprons, collars, etc.
If you don't have a towel bar above the bath, or need space for more petticoats, hang the garments from the shower curtain pole (place towels or dirty clothing along the floor side of the tub to catch drips, or you'll be cleaning starch off the floor).
As they dry, the clothes will go from wet/limp to crunchy and somewhat sticky. Every couple of hours I'll 'rotate' the hanging petticoat: pulling apart the fabric that's stuck together and hanging it again from a different place on the garment. The topmost point dries first, so I usually start by hanging it up from the waist band twice (once with the buttons to the side, once with them folded to the center); when the top half is dry, I'll switch to hanging it by the hem, switching the connection points two or three times.
When the item is dry, it will be crunchy and stiff. Petticoats can be worn in such condition, but for neat accessories (and nicer pettis), ironing is required. Some people sprinkle garments before ironing; I usually just mist with a spray bottle and iron as usual. Do not try ironing while the item is still damp from starch; it won't set right. You're better off letting the starch FULLY DRY, and then re-wetting the garment to iron.