You need some sort of unifying theme for each room in the place (or part of room, if you’re got a living room/dining room combo). And if you’re going to split up a big living room into living area/dining area/office area or what have you, an inexpensive screen or room divider will help delineate the space.
But about the theme- colors work, periods work, or other themes like sports or beer or Irish/Asian/whatever culture you like. I’ve got a pale yellow and blue French kitchen. I’ve got candles, utensils, towels, and art in pale shades of yellow and blue, with some French pictures on the wall. And everything is retro- a beehive blender, lots of chrome.
Choose one or two main colors and one or two accent colors, then keep an eye out at thrift stores, garage sales, and Target for objects like candles, pillows, rugs, or art that fit those colors.
Choose a basic style of furnishing- if you’re a traditional type, dark wood and elaborate ornaments (like feet on tables and couches) are good choices. Or you might choose natural wood. Or brightly painted wood. Whatever you like, stick with it. If you need to replace a couch or table, buy one that goes well with your existing furniture, even if that means waiting a month or shopping at every thrift store in town before you find the right piece.
Small details are easily overlooked but really pull the place together. Things like framed snapshots of your family and friends on the end table or bookshelf, candles, pillows, knick knacks, clocks, mirrors, and the other suggestions here will make your place cozier. I like old boxes, so I have some cigar boxes and others (a wooden Philadelphia cream cheese box, for example) that I keep in the living room to collect random junk. Keeps the place from getting cluttered with junk, and is decorative too. I have an old chalk box that’s just the right size for mail, so I throw all my mail in it until I can sort through it.
That’s another thing- storage is great in an apartment. Buy an ottoman that doubles as storage for magazines, the phone book, your movies or games. You get the idea. Target and other stores have lots of storage furniture available, and baskets or bins that can be used in places like the kitchen or bathroom where storage space might be hard to come by.