llevar vs vestirse (wear)
English 'wear' has no single Spanish match. Llevar is the state of wearing, vestirse is the process of dressing, and ponerse is the act of putting on.
llevar
To wear — what's on your body right now.
Lleva gafas.
He wears glasses.
Describing someone's usual look.
Llevaba un vestido rojo.
She was wearing a red dress.
Imperfect for what someone had on at a moment.
¿Qué llevas puesto?
What are you wearing?
'Puesto' makes it explicit: on you now.
vestirse
To get dressed, or to dress in a style or colour.
Me visto en cinco minutos.
I get dressed in five minutes.
The process. Stem change: visto, vistes.
Se vistió de negro.
She dressed in black.
Vestirse de + colour or role: 'vestirse de payaso'.
Se viste muy bien.
He dresses very well.
Style. Vestirse bien/mal.
Tricky bit
'Ponerse' = put on, 'llevar' = be wearing, 'vestirse' = get dressed. 'Me pongo el abrigo, llevo el abrigo' — first the action, then the state.