What are the rules for borrowing against my 401k?

The answer to your question is readily at hand in a brochure you were given at plan enrollment called the Summary Plan Description (SPD). That document will tell you under what circumstances you can borrow from your account balance and what the terms for repayment are. If you can't find/weren't given a SPD, your human resources folks can provide you with one along with the forms to request a loan if available.

Charles has already pointed you to the Summary Plan Description. I'll just add that, if your plan allows borrowing, you'll typically be limited to a loan of up to 50% of your vested account balance, to a maximum of $50,000.
This would be paid back with interest to the plan over 5 years, or 10 years if it's for down payment on a home. Failure to make scheduled loan payments causes those payments to be treated as taxable income and, if you're under age 59.5, would also be subject to the 10% federal penalty tax for early distributions.