You can either say "Agarrar" o "Tomar".

Puede obtener el perro?

Puede ir a agarrar al perro?

No creo que existe tal cosa.

Quiero agarrar tu mano para siempre.

Note! This is if you're in Mexico. In Spain you would say sujetar/coger instead of agarrar

but it would probably sound better saying it differently.

Agarrar is the most common verb for "to grab". If you are in Spain you can say "coger" but be careful where you use that because it means something very different in other spanish speaking countries.