How much can I contribute into an HSA?

For 2019, max contributions for individuals are $3,500 and for families they are $7,000.

For 2020, max contributions for individuals are $3,550 and for families they are $7,100.

If you are 55+ years old, you can also make a catch-up contribution of $1,000.

Further, HSA eligibility is determined on an individual basis (no concept of a joint account). What this means is that each person asks him/herself this question: "Am I covered under an HSA-eligible high deductible health plan?". If the answer is yes, then you can open an HSA account. The next question to ask is: "Does my HDHP cover me + at least one other person?" If the answer is yes, you can contribute towards the family maximum. If the answer is no, you can contribute towards the individual maximum.

So if you are married and covered under the same plan, technically each person can open up his/her own HSA account, but between the two of you, you cannot contribute more than the family contribution maximum (see above).

Source: Rev. Proc. 2019-27: Changes to HSA contribution limitation for 2018. Internal Revenue Service (IRS)

Source: Rev. Proc. 2019-30: HSA contribution limitation for 2019. Internal Revenue Service (IRS)