Can you give more information? Genders of dogs, ages, neutered or not, anything about their personality? Have you already taken the second dog or is it just planned? If you've already got him / her, how has dog 1 reacted?
Our dog is a 3 year old male who is neutered. He is a very loving and gentle dog, lab cross he is very lively and loves lots of play and walks. The second dog moved in yesterday 2 months old and is a girl. Our dog is ignoring her, when she walks passed he doesn't make eye contact and turns away.
That sounds very normal and fine, Slippers. For a dog, making eye contact by staring would be seen as very confrontational/aggressive. Peacefully ignoring each other is great!
Just take things very gently for the first few days, help the new dog settle into your family's routine, and make sure first dog gets plenty of cuddles and reassurance. Possible flashpoints are feeding and bed spaces - can be a good idea to feed them separately to begin with just to avoid any crowding/worries and to make sure they both have a comfy bed. Going on regular walks together will help a lot.
You'll gradually see them getting used to each other over the next few days and weeks, just as we would with a new housemate.
Your new dog will be spending the first few days in learning the ropes in her new home - she'll probably be too busy with that at first to want to play as well. As she gradually becomes accustomed to your household routine, and what's expected of her, you can expect to see more of her playful/social side, both with you and with the other dog.
Sounds absolutely fine, I wouldn't worry about forcing them. Let them get used to each other in their own time. We adopted our second girl nearly a year ago - she was an adult rescue roughly the same age as our boy (who we had from a puppy). It was quite a long time before they played together, mostly because she didn't really know how to play (ex puppy farm breeder). After a few weeks she started to interact more, and now they play all the time. My boy adjusted the way he plays though - he's usually quite rough but is much more gentle with our girl. I'm sure they'll be fine when they get to know each other. Don't be worried if your older dog occasionally grumbles at the pup - this is normal behaviour and is called a "correction", performed when pup has pushed her luck! It's not a problem so long as he doesn't make contact with her.
2 dogs are much easier than one! Mine took a while to settle as the first dog was a bit put out, but they are best pals now, look out for each other, worry if one has an injury, groom each other and play together. It's so sweet.
Don't worry if the play looks and sounds like they are trying to kill each other. There may be a lot of snarling, barking, rolling abut and mouthing. They aren't hurting each other though, so no need to intervene unless the pup is getting a bit worried and hiding.