Since you've had it cleaned, I assume the sweep told you if it is in good repair; no visible cracks in the flue, damper working, you have a grate top keep the wood off the floor, and let the ash fall away, a set of tools, a spark screen, etc.
That said, you'll need some kindling, and maybe a little newspaper to get it started. Too much paper is bad. Put the knidling in, try to lean them against each other so there is some air space around the wood. Put the paper into amongst the kindling, open the damper, and light the paper. Use a long fireplace match, or a long reach lighter. You may need to use a bellows to get the paper hot enough to light the kindling. you shouldn't try to blow on the fire, you may get a faceful of hot ash. You need to get a decent fire going with the kindling to get a flow of air up the chimny, this will keep the smoke from getting into your house. Put some small logs into the kindling, leaning them in to keep some air space, but letting the fire from the kindling run onto them. Try to get some bark into the flames, that will help get the log going faster. Let the smaller logs catch, and burn for a short while, then you can add larger logs.
Good luck, and rember, safety first. Always keep a fire extinguisher in you home.
