A common grammar construct to express you like [something] is [something]が+すきです。When using すきです, you'll mark the item you like with が.
で lets us know the location of something. More specifically, it lets us know the location where the verb action took place. In this sentence it lets us know the location that we went shopping at.
What're we writing? We're writing a てがみ(letter). How do we we're writing a てぐみ? Because we see the を after it, that's why. Place を after the thing crucial to the verb in use. If I said to you "I'm writing", you'd ask me what the heck I was writing. That what-the-heck-you're-writing needs an を after it to be beautiful Japanese.
A very useful phrase to use when you want to ask the time. This situation is terribly frequent, especially when you don't have a watch, cell phone, aren't in front of a computer, and there are no public clocks anywhere. When that happens, you'll be glad that the Japanese textbooks prioritized teaching us this phrase.