Dating after divorce is tough. Dating after divorce when you have kids is way beyond tough. So how is it that you introduce that someone new to the kids? I suppose there are several ways it can be done. The one thing I would NOT do is tell your kids that this is just a friend and we are not dating etc. if you are.
That doesn't mean you have to spill the beans and reveal all of your cards right away, but certainly don't lie about it. I have always dated someone for awhile before I even consider introducing him to the kids. After all, what woud be the point of bringing kids into it if 5 dates from now, or even 10 dates from now I discover he just isn't for me.
Once I do seem to figure that out and I need to test the waters, then I think the most effective way is to just do it without making a big deal out of it. If you often go out with other friends or have them over to your home, then invite your "date" to do something similar.
That way the new person might sort of blend in just like another friend without it having to be a big deal. I would probably pretty soon decide if you are going to continue dating the person even after they've met the kids. If so, it's best to let your kids know so they can begin getting used to the idea of you being with someone besides their parent.
If you do this a few times, it will be old hat to them, and easier on you too!