There are many ways to chlorinate an above ground pool. I use a basic blue floating pool chlorinator filled with a few three inch tablets.
It is very important with an above ground pool to never let the chemicals come in direct contact with the liner. If I let my pool chlorinator run out of tablets I always have a supply of granular chlorine on hand. I pour the chlorine directly into the skimmer. That gives the pool a quick boost of chlorine. I then refill the chlorinator and am good for another week or so. During the summer months I find it very helpful to add a bag or two of vinyl shock treatment to the pool every couple of weeks. It is also important to run the filter more hours the hotter it gets.There are many versions of the automatic chlorinators that will plumb right into an above ground pool filter system. The one on the right is one of them. This one taps into a short piece of PVC pipe coming out of the return port on the filter. It's not too difficult to install and from what I have heard does a nice job. There are also units that attach directly into the return line with the simple addition of an extra filter hose. They are probably the easiest to install but I have yet to see one come with the extra hose. In some cases, depending on the filter, they can be attached directly to the filter return fitting port. There are also a couple of versions that will hang down from the return fitting on the pool.
There are many ways to get the chlorine into the pool, from very simple and inexpensive, to more complex and costly.
Start with a floater and do your homework before investing in an automatic chlorinator. See what your neighbors are using and do some research.