"start the day" = slang phrase meaning the beginning of the day, what you did in the morning between waking up and before noon. It can refer to the time before you left your house for work or school, or what you accomplished during the beginning of work or school.
"a good start" = to begin something well, correctly, or with luck.
"a bad start" = to begin something badly, incorrectly, or with bad luck.
"one way to do something" = There are many ways to do tasks. Many possibilities. For example how can a person get to the store? "One way is to walk to the store.", or "One way is to ride a bike to the store." or "One way is to drive to the store". All are viable ways to get to a store. I want to make a painting. How can I do it? "One way is to make an abstract painting with colors". "Another way is to make a painting of mountains and a pretty forest." I am using this phrase to emphasize one path of many paths or possible outcomes.
"One way to start the day" = often used to describe an unusual beginning of a day. It can be very good or very bad.
John: While walking to work this morning, I found $100 on the sidewalk!
Amy: Wow. That's one way to start the day! You are so lucky!
Tom: This morning, a went to take a shower, but I tripped on my cat, and I fell into the toilet. My head got all wet with toilet water!"
Jen: Wow! That's one way to start the day. You are very unfortunate!