For the sake of completeness:
1. Anyone with a qualifying HDHP and no other coverage can contribute to an HSA, even if not offered by an employer. Many banks and brokers offer HSAs, although you are likely to see a monthly maintenance fee of around $3-$5 with a private HSA that you may not see with an employer sponsored account.
2. If you contribute via payroll deduction, the tax laws consider that an "employer" contribution. The legal view is that you agree to a voluntary salary reduction, and the employer contributes that money to the HSA for you. So all workplace contributions, including both voluntary contributions and employer match, are "employer contributions."
3. You can always contribute after-tax dollars to an HSA, even if it is also an employer sponsored plan, so long as you don't go over your annual limit. For example, suppose you are covered by a single HDHP and are under the age of 55. Your annual contribution limit is $4150. In January you elect a contribution of $50 per week, or $2600 for the year. You decide you have more expenses and want to contribute more, but your employer won't allow you to change your payroll deduction. You are still allowed to contribute up to $1550 from your after-tax out-of-pocket funds, and take a tax deduction. The only thing you lose is the extra savings from social security and medicare tax.
