Hi, in my ill spent youth, I was a sweep. Honest, it is prolly better to get a sweep to come out an clean the flue. Don't forget the clean out box inder the fire place. Should be a door outside on the chimney or perhaps in the basement.
I feel it is best to work from the top down. I hope you like heights. If you feel like the roof is a bit unstable of get a bad feeling get off the roof. Use good running shoes. Be sure the ladder is nice and stable on solid ground. (Sorry if this gets to basic) If you are set to do this yourself, you will need a few tools. [the first one will cost lots but if you do it twice a year, you will save.] You need a length of rope to reach from the top of the chimney to the damper opening above the firebox. Plus about 10 feet. Have a good root around in the surplus store for a large ball weight. Just like a regular fishing weight but bigger. You need a brush made for chimney sweeping. mesure the size of the flue and buy a brush just bigger. [if 6" get 7" brush] Get a shop brush and a shop vac is nice but a dust pan will do in a pinch. Also get a partical mask as the dust is awful to breath in. A cheap pair of garden gloves. Masking tape and news paper will complete the list.
Get the rope ready. Tie a knot larger than the hole in the brush about three feet from the end. Thread the rope through the brush and leave about a foot and a half slack and tie another knot. Tie the weight on the end and make sure the weight is on there good. Last thing you want is for the brush to come off the rope half way down.
Open the damper.Seal the firebox opening. Layout the news paper on the hearth and fit it so it over laps the opening by a few inches on either side and top and bottom. Tape the news paper together. Tape the whole thing over the opening and be sure to get tape all the way along the edges all the way around. Make a seal. Once done be sure your tools are set out near by for the clean up job once your back from top side. Brush, vac or dustpan, garbagebag if needed.
Well up you go.
Now then, sweeping is more than just a quick up and down. If you bought the right size brush, it should move a few feet at a time them get stuck. Lift the rope till the brush pulls just an inch or two, then drop the rope so it pulls the brush further down the flue. When you get to where you think the damper is, take care not to bash it with the weight. It's alright if you bump it but go easy. Pull the brush all the way back up and repeat the proccess again. If the flue is rectangular, move the brush to the other side and repeat.
Inside, we are ready to remove the seal around the firebox. Top to bottom pull the news paper from the brick. Go slow and careful not to stir up the dust. Put the mask on again and take up the dust from the flue. If you stick you hand up above the damper plate and to the back, you will find the shelf. clean there too and wipe the damper area off with the shop brush. Have a good look around afterward to see if there are any problems brewing. Loose morter or cracks will need to be fixed up at some point. Use "Devil's Putty" or the like to repair the firebox. If the cleanout is full hire a kid to shovel out all the ash and put it into garbage bags. Good for the garden. This will only need doing once every few years and the kid could use the $10 more than you need to get all dirty. ha ha That should do it till spring where you can go again. Remember to start with a good hot kindling fire once the fire place has been cleaned and inspected to promote proper burning and trouble free enjoyment all winter long.