For a first project make a mirror in the 4" to 10" range of diameter. It'll take a few weekends. Grinding, polishing, figuring, and coating a small mirror in 1 day can be done, but will require some experience.
In the US get the glass, abrasives, pitch, and polish from Newport, Willmann-Bell, or GotGrit. Their websites show some prices. At Newport's site look under "mirror starter kits." Outside north America there are also suppliers. --Some in Britain, Italy, Iran, and India.
Find some of the classic books on the subject. The Allyn J. Thomson book is online. The Richard Berry book is at abebooks. So are most others. The Texereau book is online (in French). The three volumes by Ingalls are good to have. The Neal Howard book is good
Grinding will tend to get the curve spheroidal.
With these smaller mirrors you parabolize in the polishing stage. You make your own Foucault testing apparatus for that. There are other tests, too, such as Ronchi, which you can do.
There are plenty of websites on telescope making.
There are 30+ telescope making courses, workshops, and clubs. Some are listed at the Stellafane website.
A few clubs (e.g. Washington and St Petersburg) have their own aluminising chambers. Most have their mirrors aluminised commercially.
--Plenty of mount styles. Stability and tracking are important.
This is not easy. It's a major commitment of time, effort, attention to detail and learning of technique. If you want to do it "for fun", go ahead. But even if you have to make the money delivering newspapers, it's easier to buy a completed mirror from an optical shop that is all set up to do it and can do most of the work by machine.
Fifty years ago, it used to be very common for people to make their own telescopes. Nowadays it has become very rare, because commercial telescopes have become relatively inexpensive. One result of this is that it is very hard to find the parts needed to build your own scope. Unless you have a very strong motivation to learn how to do this, and to track down the parts needed, I wouldn't recommend building your own scope. Because the parts are hard to find, they are very expensive, and a home made telescope will cost many times more than a commercially built telescope. Labour is so much cheaper in China where almost all telescopes are made nowadays.
Kits are available with all the necessary materials to grind and polish a mirror from Newport Glass Works. You grind the mirror blank by rubbing it on a glass tool using increasingly fine abrasives. Then you polish the mirror and figure it to a parabola using a Foucault tester. Finally you send it away to get it coated with aluminum. A shaving mirror is not made to an accurate enough figure for astronomical use, and is not a first-surface mirror, so produces double images.