What the TAs can do:

Give the student hints. “Have you thought about X?” or “Think about X or Y, do either of these remind you of this problem?” or “Hint - it’s related to that problem from lecture…”
Tell the student when something small (but not a whole problem) is factually wrong or right. For example if the student is unsure about one single summation in a huge time complexity calculation.
Suggest other problems which might help, or even make one up that might help, and walk through that one.
Suggest relevant and helpful parts of class notes to review and help the student review those. For example if a student is struggling to prove O(g(x)) you can walk through the definition and do a different example.
Tell the student if the overall framework of their answer is right or wrong. “Your overall approach looks right, but I can’t vouch for every detail.” or “I understand why this approach might seem right, but possibly there’s a nicer way.”

What the TAs cannot do:

Give the student the complete answer, or any major part of it, in any way - written, spoken, etc.
Give the student all or even most of the steps that should be done for the answer.
Tell the student explicitly if their answer is completely right or wrong.
Give the student so many hints that they’ve basically given away the answer.
Wait exclusively with the student while they work through the entire problem at office hours.

When in doubt, and notes:

The TA’s job is technically to help the student understand the material so that the student can do the problem. It’s not to help the student do the problem. Consider what the difference between those two things is. Of course there are gray areas, but the TA should default on the side of whatever they feel will help the student learn and understand the most.
The TA reserves the right to say “I’m not sure if I can give that much help, I should consult with Hervé and/or Justin”.
If the student gets too much help then their homework score may not represent their actual level of knowledge, and that will give them a false sense of security which will come back to bite them on the exam. There is a tough love aspect to this.
There are 750 students and only a small number of TAs, so we have to ensure that we can distribute as much assistance as we can. This means planting the seed to start the problem or answering a clarifying question for many students, rather than working through every detail in order with just one person.