Meeting the children

I was with a guy before and he had an 8 yo old son that was very quiet. I was very quiet also so I really felt awkward trying to talk to him. After a few obvious questions with obvious answers, we just sat in awkward silence the entire time. Needless to say that relationship fizzled away extremely quickly after that.                                                                         
                                                                         I'm with my boyfriend for two years and we finally discussed meeting the children. 4yo daughter. 2 yo son. I know we are going to all go out soon and I'm so nervous, anxious, & excited at the same time. It feels like much more pressure than meeting his mother because I know he'll be watching to see how we get along. I really adore his children based off of the stories he tells me. Plus, they are a part of him so I already love them regardless. I guess I feel weird because I know I'm not their mom and I don't want them to think I'm some evil lady trying to steal dad away or replace their mom. Any step moms or gf that were in my situation have any tips for meeting the children and bonding with them ??? What are your experiences ??