The guitar itself does not appear to be a typical classical guitar. They generally have no pick guard. The strings that are on it are classical nylon strings, though. There are two types of classical strings.
To start, all of those strings need to be replaced. When you buy them be sure to get the ones with the rings on the ends.
Many are designed to be tied to the bridge end. You don't have that kind of bridge. Those pegs you have are made to use with the 'ball ended' strings like the first ones above.
Martin, Dean Markley, Ernie Ball. should be less than $7 for a pack. buy two. classical string break a lot.
Check you tube for guitar stringing instructions.