I have older children (teenagers now). When I look back to when they were little, I just remember how hard it was. Easy to say, but try not to worry too much about whether you're doing things "right". It can be a lonely time for a mom. I actually found it easier once they were older. You're doing fine.
at this stage i think just being around you as much as possible is the most important thing. she will become independant in time when she starts school. having a secure home with her parents being good role models is the foundation. patience and calm explanations of proper manners is also the most helpful thing. kids do as they see their parents do. you sound like a caring parent.
With my two year old we do a lot of talking. A lot of pointing and naming things. Please and thank you for everything. A lot of singing and counting during car rides. Play time is great for learning. If there are shapes learn shapes. Same with colors and counting. Count everything. Like the previous person said tea parties are the best for manners. Tell her you are proud often and a lot of applauding and high fives work. Sing and dance with her and answer questions when she asks. If she looks thoughtful ask if she has a question.
I was going to add something, but I think these folks pretty much nailed it. Just remember that typically short attention span, but the more she can soak in at this age the better.
Is she in preschool? If not or if you can't afford it, I would do lots of playdates if you can to help her with socialization. Also just play with her. With my 3 year old, she just wants me to give her undivided attention and to play with her. Lots of pretending, fantasy play, coloring, etc. Do you guys go to the park? Plenty of physical activity is also great.
Take her places, any places. Kids are just like dogs. The more places they go, the better they act. If you always leave them home, they go wild when they get out. The good thing about a child for a companion, they do not really have an opinion. If they trust you, you can take them to any movie, place to eat,or on any activity, and they will be cool with your choice, so you can do anything you like.