Learn English – I didn’t understand the meaning of the sentence

Yes:

• In your first year of life you are zero years old;
• In your second year of life you are one year old;
• In your third year of life you are two years old;

And so on. If someone says "I was ten years old", they're referring to a time when they were in their eleventh year of life.

(Note that people rarely say "zero years old"; instead, they usually talk about younger children in smaller units such as weeks or months. People also rarely say things like "in my eleventh year of life"; instead, they say things like "when I was ten years old".)

The phrasal verb get over means recover from. It's often used in the context of overcoming illness, injury, or a painful experience, but I like the way this Oxford dictionary defines it:

get over (phrasal verb) recover from (an ailment or an upsetting or startling experience): ‘the trip will help him get over Sal’s death’

In this case, the person is simply surprised by his old friend's face. We don't know why (context doesn't say), but we can make some guesses:

I can't get over the way your face looks – you look so young! (surprise)

I can't get over the way your face looks – your wife's death must have been hard on you. (empathy)

I can't get over the way your face looks – where is that face painting booth? (laughter)

Any of those three are possible, but I suspect it would be the first. It mirrors what one person wrote in an advertisement for a nutrition product:

Recently I was at a gathering, and was in the company of a man I'd worked with in 2003 and 2004.
I noticed he kept watching me. Finally I went over to him, extended my hand and introduced myself.
He said, “I know who you are, I just can’t get over how you look. You look twenty years younger.”