Cycling is faster than walking. (as)
Walking is not as fast as cycling.
This tea doesn’t taste the same as the one I usually drink. (from)
This tea tastes different from the one I usually drink.
Bill’s computer isn’t as fast as mine. (than)
My computer is faster than Bill's.
This song sounds similar to a remix of an original song. (like)
This song sounds like a remix of an original song. (In this case, "similar to" and "like" are very close in meaning and the sentence is already well-constructed. You could also say: "This song is similar to a remix...")
Nicky is better at basketball than John. (as)
John isn't as good at basketball as Nicky.
Oil painting is not like pencil painting. (from)
Oil painting is different from pencil painting.
Yesterday’s exam wasn’t as short as today’s. (than)
Today's exam is shorter than yesterday's.
His new guitar isn’t different from his old one. (like)
His new guitar is like his old one.
She taught English and he taught English, too. (same)
She taught the same subject as him/He taught the same subject as her.
Nam drove more carefully than Hoa. (as)
Hoa didn't drive as carefully as Nam.