Welcome to TFP.
Please read
Pool Care Basics
Before we can tackle the algae issue, you need to have a fully functional pump and filter.
What type of filter do you have? Show a picture of it overall and also a close up of the model number and a close up of the locking mechanism.
For future reference, you can purchase a a sump pump on Amazon or at HD which will circulate your water by putting it in the shallow end and run the exit hose to the deep end. This at least lets you to keep your free chlorine (FC) up.
In order to address the algae once we get your filter operational you will need a proper test kit. See
Test Kits Compared
My concern is that the previous owner has only been using pucks which causes several things to happen over time. The CYA in the pucks helps protect the FC however, once CYA gets significantly high (over 90) the sanitation of the pool declines because the FC level is not high enough. This then causes algae to form.
So we need to know the values of critical parimeters which are
pH
FC
CC
CH
TA
CYA
Pool water temperature
It is recommended to do your own testing and not go to the pool store because those tests (although free) are not reliable due to a number of factors but mainly lack of experience of the pool store rep and cross contamination with other pool water samples.
Once you get the test kit and the results, we will need to perform the
SLAM Process.
You will need to purchase liquid chlorine (LC). Since you are in FL you can purchase 2.5gal jug of fresh LC at Pinch A Penny. Just don't purchase any algicides or other quick fix solutions they may try to sell you.
I know this is a lot to think about for your first post but those are the steps we need to take to have your pool operational then properly sanitized to rid the pool of algae.