How can I memorize functional groups?
You have to go step by step, from easier ones to complex ones.
You have to learn a lot about alkanes, alkenes, alkynes. Then you have to practice how to draw them or how to give them IUPAC name. Then start with cycloalkanes, cycloalkenes, ...
Eventually start with complex ones: alcohols, phenoles, ethers...
Here is a short list of most important functional groups.
The best way to MEMORIZE them is to use flash cards (or a computer/tablet/phone app).
The intermittent reinforcement and immediate feedback help to form the necessary memories to recall this type of information most effectively.