Do not hide him
Even before you plan a meeting, talk to your children about him. Tell them what he likes, what he does, etc. Let your children ask questions too. That way, they will feel like they know him already.
Talk to your child about him
In your conversations, say his name now and again. Gently integrate him in your child's life. Talk about the activities you do together. Slowly but surely demonstrate how much space he takes in your life so your child knows what to expect.
Between lovers, it might be good to agree on a few things for this “first meeting”
Do we kiss or not in front of the kids? How do we explain how we met? Etc. What is most important is to make everybody comfortable.
Don’t act like you met “by coincidence”
Your children will not believe you and will tell you that you lied. Nobody wants to hear lies. Be honest! Think about it, would you like to meet your daughter’s boyfriend in a mall “by coincidence”? Be honest with your children.
Plan a meeting in a neutral place
Visit a museum, an orchard, practice a sport, combine restaurant and cinema, etc. Do something special – without overdoing it – to “celebrate” this first encounter. In addition, it will create happy memories of that moment.
Clearly introduce your boyfriend to your children
"There he is! This is Mark, my new boyfriend!” Also introduce him so that each child can be introduced to him. That way, everyone will feel special instead of being part of a group called “my children”. Without necessarily telling you, your children might wonder how to call your boyfriend. You can tell them that they can call him by his first name and he will do the same for them.
He will be introduced as “mom’s (or dad’s) friend”
Your child should not feel obligated to accept him immediately as a step-dad. Do not ask about his first impression. “Do you like him?” is not a trivial question. You should give room and time to develop a personal relationship with their future step-dad.
Do not rush things!
Your child will need time to accept a new adult in their life. Especially if it is a new significant other that they will start encountering on a daily/weekly basis.