Well, I guess the *easiest* would be to play BGT. BGT (it stands for Balder's Gate Trilogy) is a mod that allows you to play BG1-TotSC/BG2-SoA/BG2-SoA wToB expansion,,,,,all as one big long game. It's a rather complicated setup if you are new to installing and playing with mods, here's the readme..
http://www.spellholdstudios.net/readme/BGTReadme.htmHowever I find BGT to be a bit cumbersome, so I just import my BG1 char. into BG2. You have to have the *FinalSave* from BG1, and copy that savegame into the Save Folder of BG2. Then when you are at the character creation screen of BG2, you can choose the option to *import*. Navigate to the BG1 save and the BG2 character creation process will find your saved PC from BG1 and use it.
P.S. Sorry, I didn't actually answer your question,,,,here goes,,, BGTuTu doesn't go from bg1 to bg2 automatically. All BGTutu does is allow you to play BG1 with the improved Infinity Engine used by BG2.