Quick answer
Я хоте́л бы заплати́ть.
ya khatél by zaplatít — плати́ть for the act, заплати́ть for the finished payment
The options
The instrumental of means
How you pay goes in the instrumental: ка́ртой, нали́чными, телефо́ном. The question Чем плати́ть? — “with what shall I pay?” — uses the instrumental question word.
Aspect
Плати́ть is the process, заплати́ть the completed act. At a till you want the perfective: Я хочу́ заплати́ть. In a general statement the imperfective fits: Здесь мо́жно плати́ть ка́ртой — you can pay by card here.
A practical note
Card payment is near-universal in Russian cities, and payment by QR code through a banking app is now common. Foreign cards may not work, so carrying some cash is still sensible — and Нали́чными is a useful word to have ready.
What you hear back
Typical mistakes
Я хочу́ плати́ть — at the till
Я хочу́ заплати́ть.
A single completed payment is perfective.
с ка́ртой
ка́ртой
The means takes the bare instrumental, no preposition.
Check yourself
Which is correct?