How to pay taxes on single owner LLC

Instead 'me' the owner of the LLC must report all profits (or losses) of the LLC on Schedule C and submit it with your 1040 tax return.

Correct, you will report your business income on Schedule C if you have not elected to have your LLC taxed as a different type of business entity.

Is this the only way to pay taxes on the LLC or can I/should I pay quarterly.

This is not an either or thing you'll report your business income on Schedule C and you will likely need to make quarterly estimated payments (this is calculated using how much you are making and how much is already being withheld from other sources of income).

Also, do I pay taxes for the entire 100k or 30k as I have given the employee 70k and she must file a 1099 on her taxes?

You pay tax on your business profit, the 70k you paid is an expense which reduces your profit to 30k (maybe other legitimate expenses can further reduce your business profit). You'll issue the party you paid either a 1099, a W2, or nothing at all, depending on their business type/employee status. In your case you indicated corp-to-corp which if proper means you would not issue any tax document to them for payments rendered.

It would likely be worth consulting a local tax professional to make sure you have everything set correctly.