Validate their feelings, give the feelings a name (people who don't have the words to explain how they feel struggle to deal with their feelings) and reassure them that you are still their Mummy and still love them just as much. I also think that managing the relationship between your children is even more important than managing your relationship with each of them.
My son was 19 months when my daughter was born, and he struggled to accept that I was cuddling someone else. He constantly clamoured for my attention whenever I had to attend to her. About 4 months in (so he was only 24 months-ish, I had a chat with him where I acknowledged he was feeling pushed out by the new baby, but it didn't mean I loved him any less, and that I had enough love and cuddles for both of them.
Now, bearing in mind his age at the time, I wasn't sure he would understand me at all, but it dramatically changed his behaviour around me and the baby - he stopped kicking off every time I picked her up.
I also took a lot of time teaching my children that they were to love each other. I would not tolerate fighting, jealousy, selfishness or anything like that - their job was to be each other's champion no matter what. I remember once I was telling one of the children off and the other one piled in and started telling them off too. I turned to the second child and said "Your job is to stick up for your bro/sister, not to join in with me. You should always be on each other's side".
My two are teens now and I often hear them saying "love you" to each other before they go their separate ways to school. 😍
But I remember that first year as being so hard. I felt guilty that the older one no longer had me all to himself, and I felt guilty that the younger one had never had me all to herself. When I spent time with one I felt guilty for the other, and when I was with both I felt guilty nobody was getting one-to-one time. So working on making a lovely bond between the siblings was one way I helped myself see the whole thing in a more positive light. Siblings can be each other's best friend for a lifetime, if you get the dynamic right in the family.