pagar vs cobrar
Pagar is handing over money. Cobrar is receiving it — as a wage, a fee or a bill.
pagar
To pay, to hand money over — for something, to someone.
Pago yo.
I'll pay.
Offering to cover the bill.
Pagué con tarjeta.
I paid by card.
Pagar con tarjeta/efectivo. No direct object needed.
Pagamos la cuenta a medias.
We split the bill.
A medias = half each.
cobrar
To charge, to collect payment, to earn a wage.
Cobro a fin de mes.
I get paid at the end of the month.
Receiving a salary. The employee is the subject.
Me han cobrado de más.
They've overcharged me.
The shop or bank is the one charging.
¿Me cobra, por favor?
Can I pay, please?
Said to a waiter. Literally 'can you charge me?'. Also 'la cuenta, por favor' works.
Tricky bit
'Cobrar' has both directions: you charge a client or you collect your salary. 'Cobrar vida' means to come to life. 'Pagar' is always the one handing money over.