I live in an apt so that's all I use. A grill pan, but many today aren't like mine. The edges or "slats" of my grill pan are raised higher and are sharper than what I've seen in stores lately, so it creates better grill marks than the flatter ones. Probably a quarter of an inch tall by a sixteenth inch at the top. I believe it's a 15 year old Lodge. That's the first thing I would look for.
I also treat it just like any other cast iron pan and don't use soap - only hot water and a scraper - and only roughly remove carbon buildup with paper towel and flame drying (setting it on the stove). Although you clean actual grill grates, I don't remove all the carbon on my grill pan. It's what seasons the pan and adds a charcoalish flavor. Fat also runs along the inside the scallops of the pan and smokes the meats. (I turn off the smoke detector and open a window). Getting it blistering hot is key for grill marks.
I put it on the stove and forget it until it smokes. Then I add the meat. But not if I'm grilling fish (lower temp and oil) or chicken. Its a matter of regulating heat the same way you would on any other outdoor grill. Same with moving the protein before it's had a chance to get a "skin."
I also use a cover that came with another pan and use it as a lid - like in the outdoor charcoal ones - if I have to finish larger pieces of meat or use as a warmer. Really big things like a rack of ribs or a shoulder I do in the oven.