How can I calculate the number of branches in an alkane isomer?
Each instance of a comma-delimited number in the prefix is directly indicating a branch on the "backbone" or base-chain. It's quite literally the number of numbers.

The most complicated example you have can be dissected like this:

$2,2,3,3-$ tells us to anticipate four branching groups from the base-chain on the 2nd, 2nd, 3rd, and 3rd carbons.

$Tetra$ tells us that all four branching groups are identical (since there are four total)

$methyl$ tells us the name of the branches. The $methyl$ group is a $\ce{-CH3}$ attached to the backbone.

$butane$ tells us what the backbone is; in this case, a 4-carbon ($but-$) fully-saturated carbohydrate ($-ane$).

So the molecule will look like this, with the 4 branches indicated: