DD can be a very exhausting little girl, so I can completely understand your question! Um, basically, we've been working on her since she was pretty little and "teaching" her how to play by herself.
Don't take this to mean that we leave her alone a lot (quite the contrary!) but rather if she starts to get interested in a toy we always fad into the background and give her space. We don't interrupt her when she's playing by herself and only join in if she asks. I also try and encourage pretend play by showing her new and interesting ways to use her toys to help her to think of new ideas on her own (for instance, just the other day we took some long neglected block and dumped them in a mixing bowl and gave her a spoon and she was busy "cooking" for awhile).
We also try and show her by example e.g. she seems us reading books to ourselves, "drawing" (ok, actually solving equations), etc. Then she does the same on her own.
Some days she just really needs us around and that's ok too. But if it gets to be too much we try and pull out new toys that she hasn't seen in awhile (we do a toy rotation).
Friendships are hard for us too. She does really well with older kids at the playground if they have patience but I don't personally know any moms with older kids so that makes it tricky. Kids near to her age or younger she tends to think they are dolls acts accordingly.
I also wanted to add. We've been really making a point of doing housework in front of DD lately. She's so not the kid that wants to sort/organize/stack but rather she wants to seek and destroy! So we've been make sure to clean in front of her. She helps to some extent. She LOVES the broom and to sweep and she'll clean her dry erase board too. Baby steps, right?
