Spoiler for 15 year old game ahead.
The transition is quite good IMHO; actually not only from an in-game point, but also from a technical point - after completing BG1, the game automatically boots up BG2, imports your old Character and starts right off. And like Stabwound mentioned, the other Characters are also kept how they were in your game of BG1. For example if you had Imoen in your party and never Dual Classed her, she won't be a Thief/Mage in BG2 but stay as you "made her" in BG1.
Storywise the setup follows the BG2 opening. You are being captured on your way to Amn.
With the Trilogy mod BG1 doesn't directly end after you defeat Sarevok. Instead, you return to the keep in order to inform Belt about your victory (he was that Council dude you gave Sarevok's Diary to and saved him last second before the Doppelgangers could kill him and the other Nobles).
When doing so, Belt tells you that things could get kind of hot in Baldur's Gate for you in the coming days, because the other surviving Nobles that witnessed your fight with Sarevok and his minions in the castle are suspecting the player to be a Bhaalspawn as well.
He reckons the best course of action is for you to get out of town for a couple weeks, while he will reason with the rest of the Nobles. Incidentally, you are also one of the few people left that can be trusted by the Council, which comes in handy because someone has to try and explain what really went down to Amn in order to prevent the war for which Sarevok sow the seeds.
Once you embark on your journey there is an in-game Cutscene where you and the party gets knocked out while meeting the - memory doesn't serve me well here... was it the messengers/guides/envoys? - well the people you were supposed to meet and have been told about by Belt.
Long story short Trilogy Transition: Dialogue with Belt - Party gets jumped and knocked out in in-game Cutscene - Fade to black. BG2 boots up, automatically imports your Character and starts you right off with the BG2 Intro, then the game starts immediately and you wake up from the fade to black in your little cage. Now playing BG2.
Click to expand...