I have learned to make/bake a cake

Today I'm very happy, because I have learned to make a cake.
When I came back from shopping this morning, I felt a little hungry. Then I thought if I could make a cake for myself, so I decided to try. I searched for a way (to make a cake) on the Internet and knew ingredients are very important. I took two eggs, some flour and a little sugar, mixed these things for about 15 minutes, then I cooked it.
Doing this thing requires patience, but it is interesting.

I have learned HOW to make A cake.

Today I AM very happy because I have learnT HOW to make a cake.
When I came back FROM shopping this morning I felt a little hungry, SO I WONDERED if I COULD make a cake for myself AND decided to try. I searched ON THE Internet TO FIND A RECIPE (OR) TO FIND THE NEEDED ingredients.  I took two eggs, some flour and a little sugar, mixed thEM TOGETHER FOR about 15 minutes, then cooked it. OR THEN PUT IT IN THE OVEN.
I NEEDED patience TO DO THIS but it WAS interesTING.  

I hope it tasted good too :-)

I'm not a native speaker, but I would write it like this:

I have learnt (learned) how to bake a cake

Today is a very happy day for me, because I learnt (learned)  how to bake a cake.

when I came back from shopping this morning, I felt a little bit hungry. Then, I thought about baking a cake for myself, so I decided to try.  I searched online and found a recipe. I knew the ingredients were very important. I took two eggs, some flour and  a little sugar, and mixed them about 15 minutes.   Then, I baked the cake.

Doing all that needs patience, but it is interesting.