There is an old pool care myth, still discussed in some places, that pouring acid quickly in one spot will lower TA, while spreading it slowly around the edge of the pool will lower PH. This is not true. Acid will lower both PH and TA regardless of how it is poured. Normally TA is only lowered by a little, for small PH changes you probably won't notice a difference. When making large PH changes at high starting TA levels the change will be more noticeable.
How you pour the acid does affect how much damage the acid can do to the pool. Acid is denser than water and without good circulation it will tend to puddle at the bottom of the pool and that can cause damage to plaster and vinyl. By pouring it slowly in front of a return while the pump is running you get it to mix quickly and throughly, thus avoiding any problems.
To lower TA you need to add acid to bring both the PH and TA down. Then you aerate the pool to cause CO2 outgassing, which will raise the PH back up without raising the TA. Adding borax will raise both PH and TA in the same proportions that acid lowers PH and TA. Adding soda ash/PH Up raises both PH and TA, but TA is raised by more than it would be if you used borax.
There is a wonderful research paper where this was explored. It includes a very detailed discussion of the chemistry involved as well as some great photographs of colored acid pooling at the bottom.
(I wrote this at the same time as Jason. We both refer to the same paper discrediting this method.)
The "slug" or "acid column" method was fully discredited here. You lower pH by adding acid slowly over a return flow with the pump running. The TA is somewhat lowered at the same time as pH and TA move together.
To lower the TA by itself, one must use a combination of acid addition with aeration and the procedure is outlined as follows (I don't think we have a sticky for this yet).
PROCEDURE .......... pH .. TA
Acid ....................... - ..... - ... Lower pH to 7.0 ( or next to lowest measurement on pH test kit, but not below 6.8 )
Aeration ................ + ..... 0 ... Waterfalls, fountains, showers, point returns up, splash, run SWG Acid ....................... - ..... - ... When pH from aeration rises to 7.2, add acid to lower to 7.0
----------------------------------- Aeration + Acid ...... 0 ..... - ... Repeat the above until the TA gets to your target ( e.g. 80 ppm )
Aeration ................ + ..... 0 ... Aerate (and no longer add acid) until pH rises to target pH ( e.g. 7.7 )
=================== Net Result .............. 0 ..... - ... Net result is lowering TA with no change in pH ( unless final pH target is different than starting pH )
In the procedure above, I describe adding acid when the pH hits 7.2 but you can do it whenever you want such as waiting for the pH to go higher. It's just faster to keep the pH lower during aeration as this outgasses carbon dioxide more quickly.