When my husband and I married, our children were 3, 5, and 7. We are an excellent integrated family now, 6 years later. My children have had two stepmoms in those years, and they had good relationships with both of them.
We were very clear with the children that "You already have a mommy/daddy. Your stepmom/stepdad is someone whose job is to love you and be there for you and help your mommy/daddy to raise you to be a good person." When SD wants me to get involved in a decision that should be made by her parents, I am very clear with her that this isn't my role. I'll offer her pointers on how to frame her argument to get what she wants (if I agree), but I'm not the right person to intervene for her with her mom or to make the decision.
As was said, respect is very important - respect for all members of the family, for the kids' other families, AND respect for the household rules. We each enforce the household rules, even with our stepkids, and we enforce them evenly. If we were to show bias to our biokids it would be noted and cause immediate havoc. For decisions that need to be made by the bioparents (like when a kid can get a phone), we are careful to explain to the other(s) why/how that decision was made and why their situation is different.
For us, I think the good relationships came from showing up. Even when we were dating, my husband attended every one of my oldest's sports games. I have attended almost every one of my stepdaughter's activities. Their other parents don't generally attend, and the kids definitely notice that. SD doesn't seem bothered by the fact that her mom doesn't appear, because she doesn't expect that, but the one time I missed a game there were major tears.
My biokids' stepmom(s) did an EXCELLENT job with finding an activity to share with the kids to bond. My D and her current stepmom paint each other's nails every time D is there. I made a point to back off those activities (and not try to compete) so that my biokids could treasure having "their thing" with her stepmom.
Part of that, in our house, is also finding something we do that we can offer to coach the stepkids in. "I'm baking a cake - do you want me to show you how to do it?" "I'm going to do some tool-heavy work in the garage - want to come help and I'll show you how to use the tools?"
We also make a point for the parent and biokid(s) to have time together without the stepparent. H and SD spend at least a few hours every week on-on-one. I do the same with my biokids. Larger "fun" things, though, include everyone. We don't want any kid to feel left out.
Patience is key. The first year we were together, my 3-year-old ran to me every time my H came anywhere in my vicinity, put his hand up in the "stop" motion, and yelled "MY MAMA". It was hilarious. H never pushed - he let S set the (glacial) pace of their relationship. When S wanted or needed something (like a refill of water), S ALWAYS asked for me to do it. After the first 9 months, if I was out of the room H switched to saying "Mommy is busy right now. Would you like to wait, or can I get it for you?" For a few months, S always said he'd wait. Finally he grudgingly decided H could help him. After H proved to be reliable at filling sippy cups and handing out snacks, S accepted him as part of our family. Now they are very close.