Like an IRA, you can contribute to an HSA separately from your employer, unlike a 401K/403b, etc. You transfer money online from your bank account (or send a check if you so choose). Then you deduct contributions on your tax return, like an IRA.
Ideally, you should direct your employer to send $X per pay period to your outside account HSA, similar to the way you tell your employer that your direct deposit goes to your checking account, because only by being routed through payroll can you save on Social Security and Medicare taxes by contributing to an HSA.
JMoody, if you and your wife can get part of her paycheck going straight to the HSA to max it out, that would be the best course to decrease payroll taxes.
For others in the same situation:
1) Max HSA via paycheck deductions.
2) Some amount of paycheck must go to remaining payroll taxes.
3) Balance of paycheck goes to 401(k) or 457.
4) Fill up IRA with amounts from personal fund as limited by your income/spouse's income.