Just to check the obvious - does the fireplace have a grate? Building the fire on a grate makes everything easier because the air flow is much better.

Make sure that you're using dry, seasoned wood. Dry wood is safer because it will deposit less creosote in the chimney. It will also catch fire more easily and smoke less. Manufactured logs are probably OK to keep in the living area, but make sure to store regular wood outside. If you can possibly avoid it, don't bring in more than you can burn in an hour, unless you want to share your apartment with little critters!

It takes some patience to get a good fire going to where you can throw on a log and leave it. I find that I need to have some nice glowing embers before I can walk away for more than 5 minutes and not have the whole thing go out. Sometimes this takes 10 minutes, but sometimes it takes an hour.