Yes, you can contribute to your HSA until April 15th. You can ask the bank (or whoever has the HSA) how to contribute to it. You will enter the non-employer contributions in TurboTax as a separate thing (the contributions through your employer show up on your W-2).
For future reference, it is usually better to contribute through your employer because it save both income tax AND Social Security/Medicare taxes (FICA).
I also want to caution you in the event you BOTH FSA contributions and HSA contributions in the same year. Unless they are specifically designed to work with each other (such as the FSA only pays after the deductible is met, or only covers dental and vision), the FSA would disqualify HSA contributions.
