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.
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.