When we speak of age, we use the verb to be, for example, "I'm 43." You can use this in the past, for example, "when I was six." You can say "six years old," but you don't have to, because people will understand that you're talking about age. However, with babies, when you're still counting months, it's customary to say "six months old."
On the day of your birthday, your age changes, and we use the verb turn. For example, "he just turned seven." We also use this with things, like "Wikipedia turns 15," which means that Wikipedia has existed for fifteen years.
With other kinds of celebrations of time passing, we often use the word anniversary. You can have a wedding anniversary, an anniversary at work, etc. For example, "yesterday was my eighth wedding anniversary."