Poner means basically to put or to place:

Pedro puso una manzana en la cesta. – Pedro put an apple in the basket.
Tus bromas me ponen de mal humor. – Your jokes put me in a bad mood.

It can also mean to turn something on (appliances, etc.):

Pon la lavadora en marcha. – Turn on the washing machine.
Por favor, no pongan la tele. – Please, don’t turn on the TV.

To write:

Puse en el examen todo lo que sabía. – I wrote everything I knew in the exam.
No hay que poner todo lo que a uno se le ocurra. – You can’t write everything you think of.

To send, to communicate:

Mis padres me han puesto una carta urgente. – My parents sent me an urgent letter.
Le pondremos un fax. – We’ll fax him.

To name:

Pilar le puso al niño un nombre bíblico. – Pilar named the boy a biblical name.
Le hemos puesto Manuela, como su madre. – We named her Manuela, after her mother.

To indicate, to assign:

Pon tú las condiciones del contrato. – You put the conditions to the contract.
Pon el precio que crees que vale y el coche es tuyo. – Put the price you believe it’s worth and the car is yours.

To consider, to suppose:

Pongamos que me invita a cenar; no sé qué hacer. – Let’s suppose he invites me to dinner; I don’t know what to do.
Pongamos que llueve… – Let’s suppose it rains…

To start a business:

He puesto una tienda de muebles. – I opened a furniture store.
Eva ha puesto una peluquería. – Eva opened a hair salon.

To broadcast:

Hoy ponen una película de Tarantino. – They’re showing a Tarantino film today.
No sé qué ponen hoy. – I don’t now what’s on today.

Poner has several other meanings and expressions so check a good Spanish dictionary for more meanings. Nos vemos prontito.