When I bought my house almost 20 years ago, they had previously installed a gas fireplace in the basement and did a sloppy job on the exhaust pipe which ran up the chimney.  The cap had been removed and the second flue had been exposed.  Only recently did I decide to fix this with a new chimney pot.  I found a masonry supply store nearby, I-XL Masonry, and brought them measurements and pictures to get the correct size of a chimney pot.  I also picked up a small bag of brick mortar at Home Depot in the US.  I could only find large bags in Canada.  Research online indicated I should be casting a chimney crown with a drip edge but this would be too much work.  I would just use the brick mortar to build a small slope on the top edge for rain water to run down.  The first step was to take down the bricks and they came down fairly easy with a small tap of a hammer.  Once I cleaned out all the old mortar leaving a level surface, I installed the new chimney pot.  I also had some scrap metal screen that I used to cover the flue to keep animals out.  I then applied mortar to put a sloped edge along the brick.  I did have to go back on the roof a couple of weeks later since I could hear clanging from the chimney on windy days.  The cap on the new pot wasn’t sitting completely flush and would rock.  I remedied that problem with a little bit more mortar to fill up the space and eliminate the movement.