Show your audience a piece of string that looks like it is tied in a loop. Cut the string in half. The trick works even better if you get someone from the audience to cut it for you. As you place the cut string in your hand and curl that hand into a fist, make sure the part of the string where the ends are "tied together" is in the hand. As two other people pull on the string from each end, one will eventually pull the string out of the fist, revealing it to be completely intact with no ends tied together.
This trick works best with about 22 inches of string. Go to the very center of this string and separate its strands from each other, pulling them out by a couple of inches. Once you twist those pulled out strands, it will make the rope look like it's tied together at that area. Trim the real ends so they are even with each other, After that, glue the two ends together with rubber cement. Use barely enough at the tips to bond them together while not having excess cement stick out. Once the cement is dry, touching the two ends together and rolling them in your fingers will work. The string will be cut near the area where it's glued together, and the "ends" are placed in the hand; when the string is pulled, the strands will unravel and reform the one smooth string.
Insert a string into a plastic straw, making sure the audience knows that the string can travel all the way through the straw. Bend the straw in half with the string inside it, cut the straw with a knife along the bend and separate the two pieces to make it clear it's in two. Lay the pieces on top of one another in one hand and then pull the string out of the pieces, revealing it to be whole.
Before performing the trick, cut a long slit in the straw; it helps if the straw is black. After you insert the string and bend the straw, and as you reach for the knife, slightly pull on the string so it goes through the slit and down to the ends of the straw; your fingers will cover up where the straw sticks out as you hold it. You'll only cut through the straw itself while the string is hidden below. As you stack the straw pieces on top of each other, use your fingers again to make sure no one sees the space in between them, so they won't know the string is intact until you pull it out.