The Gulf Stream is a current of water that is shrouded in mystery and confusion. This is all due to a lack of study of the water instead of actual lack of information available about the water.
The Gulf Stream has been studied for decades and is very well understood at this point in time. It flows from the Gulf of Mexico and Caribbean Sea, up by Florida and the East Coast of the United States, and then over towards the UK. The Gulf Stream is composed of warmer and saltier water than the ocean water it contacts, and it has its own wave pattern to it.
Now, there are a few horror stories that will commonly come out of the Gulf Stream. First, has to do with navigation; the second has to do with weather.
When you enter the Gulf Stream, you enter a body of water with on average a 3.5 knot current. There are areas that can even exceed 4.5 knots! When you are sailing East or West, you will be pushed North at this rate. The problem with this is people won't realize they are being pushed north and then get pushed off course!
If your crossing takes 10 hours, you can expect to be pushed at least 30 miles north! If you are not expecting this, you may find yourself never reaching the landfall you planned.
The second issue has to do with weather. Since the Gulf Stream has such a powerful current, any wind out of the North will kick up the seas in a horrible and fierce manner. Any north wind will produce a stereotypical "square" waves with steep faces and float tops. These waves can make the journey less than enjoyable.
The trick to avoid these waves is to only cross when the wind is blowing out of the South, East, or West.
To cross the Gulf Stream in an uneventful fashion, all you need to do is prepare to be pushed north (so start out further south than your destination) and only cross when there is no northern component to the wind.
As you cross, you will know you have entered the Gulf Stream because the water gets warmer, a new swell can be seen in the water, and the bioluminescence at night is magical!