Sleep at Home
You should sleep at your home during the times his children are with him, especially for the first few months of your relationship. This helps set a good example for the children and may help prevent an awkward situation for dad. If your relationship progresses to the point where you become engaged, you can begin to ease yourself into the home, making yourself a more permanent fixture due to the increased level of commitment.
Do Not Interfere
When you first begin dating a single father, for the most part it's best not to offer him parenting advice or criticize his decisions. If he does something you don't agree with, or lets poor behavior go unpunished, bite your tongue. As you become more serious, you may decide it's time to weigh in. This, however, should be done when the children are not around.
When your relationship is new, consider waiting a while to meet the kids. They could grow attached to you before you have time to determine the direction of the relationship. Once you have become a permanent fixture in dad's life, show kindness to his kids. Whether or not you agree with how they behave, a good relationship will depend on acceptance of his children. This does not mean that you need to accept disrespect from children. If this becomes a problem, take dad off to the side and talk to him about it. It is his place to reprimand his kids and let them know you are a part of his life.
Stay Out of It
Your boyfriend may have an ex-wife or a long-term love interest and the relationship likely didn't end on a happy note. While you may only be hearing one side of the story, try to avoid involvement in their relationship. And no matter what you may think of the children's mother, never say anything against her to them or in front of them. They could end up resenting you for it, no matter how true it may be.
Ask For More Attention
The longer your relationship lasts, the more time you are entitled to with dad. While you shouldn't expect him to be less of a father, you have the right to be considered equal in his life. If for any reason you feel you are being slighted, be honest with him; he can't know what you're thinking unless you tell him. He may be feeling guilty about the emotional effects his new relationship is having on the kids, which results in over-compensating by spending less time with you and more time with them.