Washer gets to spin cycle and stop

95% of the time, it is your lid switch.
The part that the lid makes contact with when it is closed (Litle plastic peice)
Depending on your make, Your can put a small pen in the hole and push down to verify if the piece is broken or it may be in the back part of your lid built into the back hinge.
Most local Appliance parts companies can get that part they just need the model and sometimes the serial number.
If you don't have any close you can usually get lid switch from these companies.
http://www.partselect.com/ or http://www.repairclinic.com/

Good Luck!