There are psychics and mediums who claim to be able to see and make contact with those from the other side. And although there is some interesting evidence that they can make contact, this ability has not been definitively proved beyond all doubt. If they indeed have this remarkable ability -- and they might -- it seems to be a gift that they have had all their lives. They were born with it. It's unlikely this is an ability you would be able to develop.
So although there is no certain way to go about seeing and feeling spirits, there are some things you can try, which I'm sure you've seen on some of those TV shows. You can experiment with electronic voice phoneomena (EVP) or perhaps even a so-called ghost box. There's no absolute proof that these methods are detecting ghost voices and messages, but that's one possibility.
And if you're so inclinded, and it seems you are, you might consider joining a ghost hunting group in your area. Again, there's no guarantee that you'll encounter a ghost on their hunts, but you will at least be with like-minded people who share the same curiosity on the subject. And who knows -- perhaps you'll be lucky enough to see a spirit!