Installing the pack is essentially the reverse of dropping the pack but it takes more care to align the rapidmates. Dropping out, you can't really hurt them as long as the pack is relatively level, but you can absolutely damage the rapidmates reinstalling if you don't take your time. This is always the most exciting part so unfortunately, I never remember to get pictures! I will do my best to explain the process thoroughly. You will want at least one helper for this part unless you want to make 500 laps around the car pumping jack handles one at a time.
At this point the fireman's loop should still be pulled and the 12V should still be disconnected. Everything should be off when the battery goes back in.
The first trick is to get 4 long M8 1.25 bolts and cut the heads off them to use as locating pins at each corner. Roll the pack under the car and align it visually with the guide pins and rapidmates. Position the 4 floor jacks and begin to lift the pack. As you reach the guide pins you might need to reposition the pack slightly. It will roll side to side on the jack's wheels but to move forward and back, the best solution is to bang on the wheel of the jacks with a small sledge hammer.
The guide pins should start to locate in their respective holes before the rapidmates start to make contact. Use an endoscope or bore scope or another tiny camera of your choice and try to get a visual of the car-side HV rapidmate and the corresponding bit on the battery. You want them aligned on both axis. Slip the camera into position through the left rear wheel well. If your camera doesn't have a good light on the end, you will need to try to tuck a work light up in the area somehow. Be aware that the car side rapidmate will pivot several degrees back and forth so you can reach up over the rear subframe and move it slightly with your hand.
Raise the pack slowly paying close attention to the rapidmates at the back. If they are aligned, the coolant rapidmate at the front will be close enough and it has a much larger degree of error - focus on the back. When you have the rapidmates engaged, lift the pack the rest of the way (careful to not lift the car through the pack) and install 4 of the side bolts on each side. You can remove the guide pins at the corners. Reach over the subframe with your hand and push down on both rapidmates. The car side is spring loaded so they don't always click into place on their own. Tesla has a special tool for this that levers off the subframe but I haven't used it. Not getting the rapidmates seated correctly is the most common thing to go wrong with this stage.
Now is the moment of truth. Hook up the fireman's loop and connect the 12V battery. Depending on what errors you had, you might hear the contactors close (the loud 'clunk-clunk' sound from the back of the car). When you have been working on any part of the HV system, the sound of the contactors closing is the best sound ever! If you don't hear that, you need to quickly put the 12V on the heavy duty charger you used to get the error codes and SMT data way back at the beginning of the process. Get in the car and put your foot on the brake to start waking things up.
The next steps depends a lot on what happens as the car wakes up. If the contactors closed, you are in great shape. If they didn't, it doesn't mean bad news, but you might need Toolbox (Tesla's subscription based PC Software suite) to reset things. The thing you want to confirm right now is that the car can communicate with the BMS - that you, at worst, have the errors you started with. You can go into service mode and check those or connect SMT and read the battery information. If you have a BMS-MIA error, you don't have the rapidmates seated fully or something else has gone wrong. Assuming you have a good connection - In Service Mode, there is a coolant air purge routine you should run. Have a jug of G48 ready to top off the coolant reservoir. It is not unusual for it to suck down another half gallon at least.
The coolant air purge routine isn't perfect. It is common to have bubbles in the system when you are done. Don't be alarmed if you get a temperature warning or two from different systems like the drive inverter or onboard charger. As you drive the car, these will burp out over time. I recommend driving the car for a few days with the frunk liner out so you can monitor the coolant level and get to the 12V battery if easily if something goes wrong.
This is a good time to install the rest of the fasteners. Get the rest of them started and torqued down to the specs in the image below. Once you have all of them in, remove the jacks, and lower the car onto the ground. Keep the rear jacks handy so you can put the bottom cover back over the rear of the car. When the coolant purge routine finishes and top the coolant up to the fill line and close the frunk. As mentioned, I like to leave the frunk liner out for a few days to watch the coolant level. The next steps will depend on what errors got you here.
A quick review of the common errors:
BMS_u018 will clear without toolbox. This error can occur with the C26/C27 failure when the caps are showing a large imbalance but haven't failed yet. When the car wakes up, SMT will show good values but the error will persist. The contactors should be closed so the DCDC is charging the 12v but you will still have the range reduced error. If all that is the case, leave things overnight and the error should be gone in the morning. The BMS takes time to reassess everything and you can't rush it without Toolbox.
BMS_u029 builds in the BMS over a period of time and needs to be reset with Toolbox. This is the 'more-bad' error that isn't automatically the C26/C27 capacitor issue.
BMS_f107 happens when the BMB reports no voltage on one or more bricks. This error latches and will need to be cleared with Toolbox. This can happen when a sense wire falls off (more common on v2 packs) or when C26/C27 fail completely and show NO voltage on the last two bricks. Wet v1 packs can also have the bottom sense wires actually come loose.
BMS_f123 happens when there is water in the pack. If you dried everything out correctly, it should clear on its own.
GTW/BMS Mismatch might be present if you are swapping packs. First, try reinstalling software in Service Mode. If you have MCU2, it sometimes works without Toolbox.
If the car runs but will no longer Supercharge after the pack installation, it is likely that the low voltage rapidmate isn't seated completely. There are several anecdotes that have been shared in the forums and on Facebook where this was the situation and pressing down on the rapidmate was the 'fix'. This is also the first place to look if you get BMS_MIA.