My dd is 2, and I am a sahm. As she is my second, I have realised how much more relaxed about what I'm doing with her, as you realise, as above poster said, everything is a learning experience for them. I'll list some things we've done regularly over the past year, their ability for play really kicks off at 18 months,nome won't be appropriate yet, but gives you an idea. Some days we just scribble, sit and play with cars or dolls etc, and that's good too!
Here's some of the stuff we do on a typical week:
We go to the park
Play hide and seek
Make dens out of blankets, cushions
Read books (rhyming ones and lift the flap kinds are great for one year olds, mine both loved Spot, Julia Donaldson's Acorn Wood series, Dear Zoo etc)
Visit the library
Go to the shop and talk about what we're buying
Playdough with shapes (now she's older, she enjoys helping to make it too)
Baking
Small jigsaws
Orchard games are good for colour and shape matching, counting. Mine love Shopping List'
Crayons/chalks/finger paints
Washing up
Pretend cooking
Dressing up
Helping mummy with laundry, making sandwiches, sweeping, vacuuming etc
Toddler group occasionally
Foam letters in the bath
Listen to music, dance, sing