You can usually splice it with a piece of scotch tape, just make sure not to put it on the side of the tape that touches the heads or you could damage them. I'd only use this method if you can't find a splcing kit. Usually if you cut the tape with a scisors diagonally and then match up the 2 sides you will get the best hold.

Scotch tape leaves a mess. Avoid it at all costs. It ozzes out over time and will ruin more and more footage. Radio Shack should still have the proper HARD adheasive repair tape for repairing audio cassettes and 1/4 inch reel to reel audio tape, and such. Used to cost about $1.50. Don't get something for repairing 8 or 16 mm film reels.

Unless the tape made a perfectly clean break that can easily be realigned, you will have to cut the ends to make a perfect match.

Before handling the tape, wash your hands well, or use unpowdered surgical gloves. Wash a brand new double or single edged razor blade, carefully, to remove lubricants.

Take the ends of the video tape and over-lap them about 1/4 to 1/2 inch. The smaller the better, but you must have a FIRM grip when you take a razor blade and cut through the pair at about a 45 degree diagonal. The diagonal is important. Then take only about 3/8 inch of the proper repair tape and stick them together on the side AWAY from the heads. Very important. Away from the heads.

If your razor is magnitized, it will leave a little pop. Sissors are almost always more magnatized than the typical clean new razor blade, and don't make as clean a cut, either. Vegas can do a point edit to eliminate the pop, but the smaller the better.

Good luck!