This is a list of activities I do with my kids at home (ages 1-2)that I posted in my personal blog. Some of these will be repeated in greater detail later on but I thought I should include it.
1. With my son who is 21 months I usually have the do-a-dot set out for him to dot away on paper. This is really enjoyable for him and if he gets bored we can color with crayons and markers too.
2. I make play-doh at home, that way I know it is safe to eat, and we play with that and some cookie cutters.
3. I let each of my boys go outside with paint, paintbrushes and a canvas to paint a masterpiece that I hang on my walls for them to proudly see. This I do outside and then hose them down afterward.
4. I take him/them to art museums in town. This isn't at home but thought I would mention it.
5. I do a lot of crafts with my older boys and my younger son likes to "participate" so I always have glue, string, paper, pom pom balls, foam pieces, fabric, etc so he can make his own craft projects. My 2 yr old especially likes to make paper bag puppes or sock puppets. They generally don't like any creature that I have ever seen but he loves doing it himself.
6. Put him in the high chair and let him splash around in "mooshy foods" like pudding. This is lots of fun and seems so forbidden. You may want him or her moved to the kitchen or outside in case of food flinging.
7. I let him tear paper and cut paper. This is usually just done in strips but it is enjoyable. We love to tear paper.
8. We also love to stick stickers on paper (and ourselves)
9. You can make musical instruments out of arts and crafts and then let your child play with them.
10. We love stamps. You can buy stamp sets (lakeshore learning has great sets) or just make them out of cut up fruit (apples and potatoes work well) or cut up sponges, use cookie cutters, etc.
11. Mix up some water with food coloring and then put it in ice cube trays to freeze. When they are taking a bath put the ice cubes in with them and they can play and let them melt. Warning: some of these might stain so keep the mixture ratio of a lot more water than food coloring. Of course if it does stain it isn't the end of the world. You can also freeze toys into the ice cubes as well. (This is debatably art) I thought about filling a tray up with blue ice cubes and a tray with yellow ice cubes. dropping them in a bowl of water to see what color they make.
12. You can buy contact paper and then half pre-cut shapes of paper. Then they just drop the shapes on and it sticks. You can stick another piece of contact paper on the other side and then you artwork is finished.
13. I bought blank thank you cards and then had my son "decorate" the exterior with finger prints and whatever else from the above list interested him. This is a fun and personal way to make thank you cards (especially if the thank you is something from your child)
14. Chalk. You can create anything with minimal mess when you use chalk outside.
You can also google words like toddler art or baby art for additional ideas. The best advice I can give for this young age is that you need to enjoy the process of making the art rather than the end result. If you are focused on what the craft should look like you won't be satisfied.