How do expenses work for an LLC with two 50/50 partners?

"The LLC will report the expenses to the IRS and report how much revenue it gave to each partner to the IRS. Then on my personal taxes I pay taxes on top of the revenue received and I don't have to worry about the LLC expenses. The expenses will be handled by the LLC taxes."

I don't think you understand what goes on here.

You have a partnership and for income tax purposes a partnership is a "pass-through entity."   Being a pass-through entity as two significant effects:

1. Pass through entities pay no income taxes even though they do prepare an income tax return.  (Form 1065 in the case of a partnership.)
2. Pass through entities "pass through" all of their business activities to the partners so that the partners can report those activities on their own income tax returns.  It's important to understand that the pass through of business activities is independent of the distribution of cash.  If the partnership has a profit then each partner will report their share of the profit even if the partnership has made no cash distributions.

As part of the preparation of Form 1065 Schedules K-1 get created - one for each partner - and each partner then enters their Schedule K-1 into their own income tax return.

It sounds like you're new to this "partnership" situation and you've not said who is responsible for preparing the partnership's income tax return, but I'd advise you not to try and prepare the partnership's income tax return yourself, at least initially.

Thanks, Tom. But how about expenses of the LLC, that were reimbursed to the partners (travel, etc.)? Is this handled on the business tax return or in the personal tax return?

If it's an "accountable plan" - you submit receipts for business-related activities - then the reimbursements are not income to you, they are business expenses reported on the partnership's income tax return.  And since you don't report the reimbursements you also do not report the expenses on your own income tax return.