An SSD is like a Hard Disk Drive (HDD), a storage device, but can access and write much faster allowing for much much faster data access. Because of the faster access if used for the Operating System (OS) the boot speed and OS operations work much quicker. IF a game is installed on the SSD the load times are decreased dramatically allowing for less lag from data access (loading new parts of maps).
Installation is simple and how will depend on what type of connection you are going to use. New motherboards, Intel and AMD now both have M.2. connections that allow for a Ram stick like SSD to be connected and mounted directly to the motherboard. Here is a pic of an M.2. socket and a M.2. SSD along with an article that will help explain in more detail: https://arstechnica.com/gadgets/2015/02/understanding-m-2-the-interface-that-will-speed-up-your-next-ssd/
the next type and most used is the same connection as a standard HDD, a SATA connection. using a SATA cable it connects to the motherboard in the same way as teh HDD's do but there size is smaller. AN SSD is 2.5 inches (2.5") wide where as the HDD's are 3.5" wide. Newer cases come with an adapter or a 2.5" slot already manufactured into them but if it does not you can get an adapter to allow the SSD to mount into a HDD bay. Some SSD's will cone with an adapter but if not here is a pic for reference:
https://www.newegg.com/Product/Product.aspx?Item=9SIAASP40M7763&ignorebbr=1&nm_mc=KNC-GoogleMKP-PC&cm_mmc=KNC-GoogleMKP-PC-_-pla-_-Accessories+-+Storage+Devices+%28Tape+-+Zip%29-_-9SIAASP40M7763&gclid=Cj0KEQjw5YfHBRDzjNnioYq3_swBEiQArj4pdBD8RlxyMnCCNFTdX2E_7fgFEqzEE68d0hlI5jjnTYMaAswB8P8HAQ&gclsrc=aw.ds
They are very simple to install it does get slightly more complicated when you try to move the OS onto it. But that is another issue totally.