(If you just want to do it without knowing why it works the here's how it's done. To prepare lower your tank temp to lower 70's. When you get the box in, cut the bag open and squirt some Amquel and Prime into the bags. Remove the fish and put them directly into the tank without acclimating.
Ammonia can be measured in two ways amount and toxicity.
Those test strips measure the amount of ALL ammonia.
Toxicity refers to the amount of un-ionized ammonia (un-ionized is a less stable molecule and is more likely to bond to something or change into something else to fill it's electrons)
When is ammonia un-ionized? It's a direct correlation between the temperature and pH. If you would like to read more into it then you can google ammonia toxicity, and read up on website's.
http://www.thekrib.com/Chemistry/ammonia-toxicity.html
Table 1. Un-ionized NH3 as a percent of total ammonia (by temperature and pH).
Percent NH3 of total ammonia
Temp (F) pH 6.5 pH 7.0 pH 7.5 pH 8.0 pH 8.5
68 .13 .40 1.24 8.82 11.2
77 .18 .57 1.77 5.38 15.3
82 .22 .70 2.17 6.56 18.2
86 .26 .80 2.48 7.46 20.3
Lets go through the stages of the fish shipment. First the fish are already in a 7.2 pH (our water) as the fish breaths and poops, it releases CO^2. If you've ever dealt with a planted tank and CO^2 you will know that it will lower the pH. You can assume that the fish are now in a pH of < 7.0. Also during shipment the temp drops to around 68 F, which is cold but will not harm any of the fish; this brings the toxicity to lower levels with the same amount of ammonia.
When the fish arrive and you open the bags the first thing to happen is gas exchange and temperature rising. CO^2 is exchanged for N^2 and O^2 gasses. This in turns raises the pH back to its normal state around 7.2. If you add water (Drip and Float Method) to dilute the ammonia you are "raising the temperature" making the ammonia more lethal.
pH and temperature change can be more tolerated. Most fish are tolerable of a jump 10F warmer and 5F cooler. pH change will effect your fish for the next week regardless if it's drip or squirt dump..... Quite pointless unless it's more then 2 points, in which case I would squirt poor a cup into the bag and then put the fish into the tank. This is replicated by the rainy season in the Amazon where temp, dH, DO, and pH all fluctuate rapidly.
The chemicals in Prime and Amquel (As well as all other ammonia chemicals) are not ammonia removers. They are ammonia detoxifies. They were not intended for household tanks but are often sold that way. They were originally made for the purpose of importing wild fish that were vulnerable to ammo burn like Apistogramma and tetra.