When can I start doing my taxes, generally speaking? Vanguard has a big long schedule of when they release tax documents, none of which make sense to me. Also waiting on my W-2 from my employer.

Based on what you wrote above, you should probably be getting a 1099-DIV from Vanguard with information about the dividends that your stock fund generated. If you have a brokerage account (as opposed to a mutual fund account), you should receive it next month.

It was a 1099-INT form. Is this essentially "interest" income that needs to have taxes paid on it?

Yes, you will include it in the total interest earned on your tax return. If you earned more than $1,500 you will put it as a separate line item on Schedule B.

Do I have to pay capital gains tax on my stock fund? I understand it is just on "sold" assets but doesn't a company like Vanguard buy and sell millions of stocks and bonds as a part of my investment through their company? Do I only pay for selling if I turn the asset fully liquid?

Mutual funds sometimes have capital gains distributions which you have to pay taxes on even if you didn't sell, due to selling gains in the underlying stocks. Index funds don't tend to have many of them, however, so it depends on what you are invested in. Otherwise, you would only pay taxes on a gain when you sold shares of the mutual fund.

How do I report my Roth IRA on my tax forms?

This is not reported on the tax return. You do want to keep a record of your contributions in the event you want to withdraw your contributions before reaching age 59.5.

doesn't the gov't need to know that I didn't exceed the 2014 contribution limit?

I'm not certain how this works. Some people run into problems when they move their IRA during the year, and the new custodian doesn't know how much you've contributed already for the year.

Will I just be able to punch all this into TaxAct and it'll figure everything out for me?

Your tax return is not too complicated, should you should be fine.