There are couple of things to start out with and reading the sticky posts in this topic is a good start but I'll recap some of it here.
You can investigate yourself if the pearls are real or fake. First of all, you should find out what the clasps are made of. Basemetal points toward fake pearls. Then you try to rub two pearls gently together. If the feeling is slightly gritty, it's likely to be real pearls. If it feels very smooth, it's likely to be fake pearls. You can also take a loupe and look at the surface. Fake pearls should have a very smooth and even surface and real pearls a less even one. You can also look at the drill holes. Fake pearls usually have larger holes and a build-up of material around the hole.
Once you know you have real pearls, the next question is what type. That is sometimes very easy to answer and sometimes not at all easy. You start by looking at the size. White pearls can be freshwater, Akoya and South Sea Pearls. SSP are generally noticeably bigger. Freshwater pearls used to be easy to spot because they often were slightly potato shaped but new FW pearls can be very round. Since you seem to have taken an interest in pearls, I recommend browsing vendor webshops and look at the various types to get a feel for what they look like, including possible sizes.
As for value, it's often a lot less than we think. It is a myth that pearls are valuable. They may be expensive to buy but the resale value is low. The best way to get an estimate is to look for finished sales on eBay of pearls that were actually sold. On this forum we don't give estimates.
Welcome to the world of pearls!