For tapping holes First you must use the proper size drill,for that you referance your handy chart http://www.brokenbolt.com/images/starrett-inch-metric-tap-drill.pdf
For example a 1/4-20 requires a #7 drill,but you can also use a #6 or a #5 thread strength is still there and its easier on the tap,any bigger than that and you lose too much thread strength.
Drill hole straight,preferably using a mill or drill press,can be done by hand,then lube up tap making sure it stays straight and go to town,thread it in and backoff and clear chips as you go especially in a blind hole or deep thru hole.
A die is used for cutting new threads,can be used to clean up threads as well. Most tap and die sets you find around are carbon steel which arent that great(depending on the threaded material) but if you dont use them often work just fine. HSS is preferred but you will pay more best for sizes you use most,as with taps make sure to use some cutting oil.
To fix stripped threads you need Helicoil(thread repair kit) kits of the proper size,they come with what you need. just dont try and use the helicoil tap also known as an STI tap to tap your regular holes or you will be hosed. Also you can redrill and retap to a larger size if possible.
The Gearwrench tap and die handles are awesome i have a kit https://mechanicguides.com/best-tap-and-die-set/ of those and many other styles. The Gearwrench die stocks hold hexagon dies,there are round ones too so be wary of that. Ive tapped and threaded and rethreaded thousands of holes over my career.
Here's a vid i found on youtube for you: