A start up with 10k award, formed LLC, now how to pay my tax

I have a start up that received 10k award from a business competition. I formed LLC to start my business, now my question is how can I minimize my tax reliability.

1) Should I state in my return that I loan my startup 10k for this business (if so how)
or
2) This is income to my business, if so how do I file this?

About myself, I'm a recent graduated student with no income or work, I have $11k of student loan on me (which I can pay off monthly in 10 years).

Recently I used turbotax, but it shows that I still have tax reliability for federal return, since $10k is my only income for the year and I am independent for the past two years already, did I do something wrong here?

The simple answer is to spend the money. You have one year to spend the $10K you won. It shouldn't be hard. Wasn't the point of the prize to help you finance your first efforts? Did you buy a computer? There you go. You pay taxes on the profit.

1. In California an LLC or an S or C corporation has to pay $800 in minimum taxes irrespective of profit. However, this is waived only for the first year.
2. LLCs are flow through entities, so gather all offsetting expenses that have taken place to drop your taxable $ amount. If you bought stuff before the LLC formation, those are also collectively put in a bucket called pre-incorporating expenses (as long as it WAS for the pursuit of profit for the business). Even if you don't have income, gather the negative income - you can carry it over to offset next years profit (hopefully!).
3. Was the $10K given to you or set aside to be given to the LLC once it was formed? You should check with a tax professional because one might count as income and the other might not. I'm NOT talking about Turbo Tax online or the run of the mill TurboTax helpers. Since you formed an LLC, you have a business account (I'm assuming US here) - call the bank and ask them for an accountant's referral/phone number. They usually have their contacts to assist businesses with such requests. Non-CPA accountants are cheaper - you don't need a CPA level accountant. In CA you might be able to do this under $200-300 for filing LLC returns for simple pre-revenue companies
4. The fee you'll pay the accountant is well spent. It will also be a business expense that you will claim later on (next year).