So you've decided to spend your vacation falling into a black hole, just to see what it's like? Good choice. Here are the highlights of what to expect:

First, you must locate a black hole. There is certainly a black hole at the center of our galaxy, but you don't have enough vacation time saved up to get there. So, look in the local vicinity for places of high X-ray emission. No, the local clinic just won't do.

The next step is getting to the black hole. Assuming you can afford a spaceship, the nearest ones are tens to hundreds of light-years away, but you can save time by accelerating yourself to relativistic speeds and taking advantage of time dilation. It does eat up the fuel budget a bit. though.

Once you've arrived, you can start falling in. The first thing you will notice is other matter falling in with you. Although there may be black holes without matter falling into them already, you won't have detected them because the X-rays we mentioned are emitted from the infalling matter before it passes the point of no return.

If your black hole is spinning, the matter will have formed into an accretion disk around the black hole's equator (it has one because it's spinning). If it's not spinning, it will be falling in from everywhere. This will be inconvenient since you don't want it to touch your spaceship: It's probably at a temperature of several million degrees.

Now's where the fun begins. Assuming you avoided the other infalling matter, as you get closer, you will begin to feel like your head is pulling away from your feet. This is due to tidal forces: The black hole has a strong gravity field, but this field grows much stronger the closer you get. Assuming you're falling in feet first, the hole is pulling harder on your feet than on your head. You must switch on your antigravity1 in order to keep you and your spaceship from being pulled into a big piece of metal spaghetti with a bit of nasty liquid somewhere inside.

Another thing you will notice is that the radio broadcasts have slowed down. You will think you're listening to Camille Saint-Saens' turtles when you're really listening to Jacques Offenbach's Orpheus in the Underworld2. This is time dilation again; only instead of saving you time, it's costing you time. You have a chance of turning around and going home, but you had still better call your boss.

As you get closer still, you will notice the black hole. Well, you'll certainly notice a big nothing, where there aren't any stars or blinding white light from the accretion disk.

You will also notice that the hole appears to be growing alarmingly fast, much faster than you might expect from simply getting closer to it. This is the black hole's gravity field again; it's so strong that it bends the light that manages to escape. This bending of light makes the hole appear to take up much more of your field of vision than it really does.

Eventually you will reach a point, 1.5 Schwarzchild radii from the hole, where the black hole appears to take up half the sky: An unbroken black wall that stretches to infinity in all directions3. As you get closer still, the rest of the Universe appears to take up increasingly small parts of the sky.

Eventually, the Universe shrinks to a blinding white pinpoint behind you. This may put a hole in your spaceship as it is all of the radiation emitted by the Universe until its heat death4. Oh, I forgot to tell you, due to time dilation the entire remainder of the History of the Universe has passed while you were malingering round this thing. I expect your job will have been filled.

At some point you will cross the event horizon of the black hole.  If it's a spinning black hole you may (according to one theory) be spat out of a white hole5 into a brand new Universe.  But as we've discovered, there's no going back.

1I hope you remembered to have antigravity installed.
2Saint-Saens' piece was a parody of Offenbach's piece,a can-can dance slowed down to a crawl.
3The other infalling matter will provide illumination, falling beside you in a kind of endless vertical meteor shower.
4At which point, the pinpoint of light will go out.
5I don't much go for this white hole nonsense; time dilation being what it is, I expect all of the infalling matter will have been reduced to primordial quantum soup and emitted into the new Universe at the same time.  All of it at the same time.  Sounds like what they call a Big Bang to me.