Once you own it bring the registration card to your gun club and have them call for your LTATT. The staff at gun clubs have far more regular contact with the CFO's office than you or I and know who to talk to to get it moving.
This is specific to Ontario. In the rest of Canada a person is allowed to get their own LTATT.
Tonysa13, the rules vary from province to province, posting your location in your profile can help get you more information that's relevant you you.
Buying new and buying used are pretty much the same, the seller calls the CFO and initiates the transfer to the buyer and is given a reference number. The buyer may or may not need to call the CFO to provide information to complete the transfer, this is where you'd need the transfer reference number.
Then, an indeterminate amount of time later the transfer will be completed, and the seller will need to make arrangements to get the gun to the buyer. You could arrange to have a courier pick it up and do door to door service, in which case no special ATT is needed since it is the courier transporting the firearm. If the buyer needs to pick it up from a depot or post office they will need an ATT from that location to their house. If the seller needs to bring the gun to the post office or courier depot they will need an ATT from their house to that location.
In all cases I've heard of, the CFO will make such special ATTs last as short as possible, so if you get the ATT for Friday night, but work late and can't make it to the post office you will need to wait until Monday to call in again and request a new STATT.
In all cases, read the fine print on your ATT. What someone else's says has no bearing on what yours says or permits you to do. "Normal" ATTs vary from province to province, and in some cases from person to person. Doublecheck what yours says, if you violate it and get caught you will face criminal charges, even if the violation only occured because of a clerical error on the part of the CFO.