i'll try and clear it up for you.
you CAN do everything you said, however, heres where it gets more complicated.
mixing ram is always a risk, some ram just doesnt work with other ram, even of the same brand. the only way to have the best possibility of getting them to work is to buy the same speed, timings, and voltages.
if you have a 4gb stick right now, you are running in single channel mode. everything your computer does goes to that one ram stick. If you add a second 4gb stick, and if it works (which it can) you will run in dual channel mode. this provides a big performance boost, especially with whatever processor you have (a-series im guessing) just make sure you put the sticks in the same colored slot, and the sticks are the same size/timings/voltages/speed etc.
it would be best to buy 2 8gb sticks if you want to upgrade. that will give you 16gb of ram, which is the most ram any gaming/web browsing type pc will need.
you can attempt to increase your ram even more if you have 4 ram slots. you can try buying the same voltages/timings/speeds as the 4gb stick you have now, in a dual channel kit (2 8gbs) and a single 4gb stick. Then, you can put the ram in this order: 8gb/4gb/8gb/4gb and that will still enable dual channel ram, and give you 24gb of ram