Watashi wa kare no shukudai wo tetsudatta.
I helped him with his homework.
Ryouri wo suru no wo tetsudatte yo.
Help me with cooking!
Watashi wa chichi ga sensha suru no wo tetsudatta.
I helped my father wash the car.
The basic pattern for 手伝う is AはBを手伝う, where A is the person helping, and B is the act that needs helping (not the person that needs helping). It is also possible to show the "direction" in which help is given by using ～てもらう、～てくれる、～てあげる.
Watashi ni tetsudatte moraitai desu ka?
Do you want me to help? (lit. Do you want to receive help from me?)
手伝う can also be made more polite by using the form お手伝いする.
Houkago, o tetsudai shite kureru?
Can you help us after school?
Daidokoro de mama no otetsudai wo shita no.
I helped mama in the kitchen.
Kanojo wa tasuke wo hitsuyou to suru.
She needs help. (Lit. As for her, help is considered necessary.)
Dare ga watashi wo tasukete kureru no?
Who will help me?
Note that in most cases, the pattern is AはBを助ける, where A is the person helping, and B is the person being helped.
助けに来る "tasuke ni kuru" is also commonly used. It means "come to (someone's) rescue".
Daremo watashi wo tasuke ni konakatta.
No one came to my rescue.
The direction of help can also be indicated by ～てもらう、～てくれる、～てあげる.
Tomodachi ni tasukete morainasai.
Get a friend to help you.
Watashi wa kare wo tasukete agetai.
I want to help him. (Lit. I want to give him help.)
Miura, Akira. Essential Japanese Vocabulary, Tuttle. See Foreword and entry on 助ける.