felvesz – to put on
Felveszem a kabátot. – I put on the coat.
Felveszik a famert. – They put the jeans on.
levesz – to take off
Leveszem a kabátot. – I take the coat off.
Leveszik a farmert. – They take off the jeans.
Talking about your shoes you can also say: felhúz
Felhúzom a cipőmet. – I put on my shoes.
Leveszem a cipőmet. – I take off my shoes.
NOTE!
Felvesz and levesz are phrasal verbs: fel + vesz AND le + vesz. As vesz is irregular in the past tense, you should pay attention to it: vesz > vett
Levettem a pólót. – I took off the shirt.
Felvettük a zoknit. – We put on the socks.