Sorry, this answer seems rambling, but it's all necessary.
The last-month rule states that you can use the full annual HSA contribution limit, if you are under HDHP coverage on December 1st of the year. This is easy - your limit is either $3,450 (Self) or $6,900 (Family) plus $1,000 if you are 55 or older.
But if you fail to keep under HDHP coverage for the following year ("the testing period"), then your full annual HSA contribution limit is revoked for the previous year (when you used the last-month rule), and the limit is recalculated.
The recalculated limit is the limit that you would have had if you had not invoked the last-month rule. In the simple case, you add $3,450 for each month you had Self coverage and $6,900 for each month you had Family coverage, add up the months, then divide by 12.
For example, let's say that you started Self HDHP coverage on July 1st. This means that you had six months at $3,450 each month for a total of 20,700 divided by 12 which equals $1,725.
So when the limit has been recalculated, your prior year contributions are applied against it to see if there were any excess contributions using the recalculated limit. If so, you are penalized.
The penalty appears on line 18. This is the would-have-been excess contributions (but for the last-month rule) which get added back to income on line 21 of Schedule 1.
The recalculation of the limit can become confusing if you switch from Self to Family or vice versa during the year or go on and off the HDHP or if some of your limit is allocated to your spouse, but this is the general idea.
