In most construction the chimney is not attached to the frame of the house
. And this makes the area around the chimney vulnerable to leaks over time as the house settles. If you are noticing water spots on the ceiling near the chimney area, it is a good indication that there is a problem with the chimney flashing. And it might be time to make some repairs.
To the untrained eye repairing or replacing the flashing around a chimney might look to be a fairly straight forward and simple job. But it is important that the job is done correctly and there are some important factors that must be taken into account. Also it is also not going to be a quick project, plan on it taking a whole day. If your roof is made of wood shingles or asphalt tiles it is feasible to perform the repair for yourself. However slate or tile roofs are more complex and best left to a professional.
The metal must fit very precisely and cutting and bending it on location up on the roof at the time of installation is not practical. The best plan of action is to make some good measurements and take them to a metal shop with experience cutting and bending chimney flashing. This will cost a bit, but will save you the cost of investing in some of the specialized tools required for the job. Otherwise you will need to obtain a pair of straight-cutting tin snips.
Some other tools that will be needed are a masonry bit and a pry bar to remove the old shingles. And don't forget about the new replacement shingles. In addition you will need a roll of ice-and-water barrier, two tubes of polyurethane caulk and some drive-in expanding anchors.
Once on the roof be sure to make safety your first priority. Although going up on a roof is not really too dangerous, it does have it hazards. Be sure to wear shoes with good traction to prevent slipping. And be aware of any power lines that might be in the area. If the roof has a steep slop to it, some toe holds and a safety harness may be required.
So it might take a good bit of research and an investment in some tools but if you are up to it, you could save a big chunk of money doing it yourself and you will surely end up learning something valuable in the process.