How do airports charge airlines for using their gates?

Some of those charges are wrapped into the landing fee, while others (like IT/network connectivity) will be separate. Some include:

~$4,000 landing fee based on the OEW + 5% fuel being 340,000lb at $9.11/1000 lb (for an A350).

~$800 for up to 8 hours at a gate (or a flat rate of $36,000/mo per aircraft for a frequently visiting ship).

~$1,000 for common use of terminal facilities (for airlines that don't have dedicated terminals - often with internationals, where they have the common check in area that is used by multiple airlines).

And that's not all the charges the airline gets from the airport, that's just the majority of the charges for "1 aircraft, 1 landing/departure" at SFO.