Repairing a broken telescopic antenna is a task that can be performed without tools, in some cases, or with little more than a screwdriver in others. Making an improvised antenna or altering the radio case for a new antenna takes more work and a few more tools. One caution should be noted, and that's the difference between receiving and transmitting antennas. Nearly any conductor will work as a receiving antenna, but a transmitting antenna is tuned to the output circuit of a radio, where the use of the wrong antenna will cause damage.
Remove a threaded antenna by unscrewing it from the radio. This type of antenna is often found on scanning radios. If it broke off near the case, try to turn it out with a pair of needle nosed pliers, or unplug the radio and take the top cover off, then remove the antenna. Take the stub with you to get the right thread size on a replacement antenna.
Replace a screw mounted antenna by removing the mounting screw. These are often found on portable radios. Take the broken stub with you to be certain a replacement antenna will fit properly.
Find a replacement ball mount antenna, although the part is sometimes hard to find. These antennas extend from inside a radio, and then may be tilted via a ball and socket base assembly. A replacement part will most likely come from the original manufacturer. With an old radio, finding that replacement may be impossible.
Improvise a replacement antenna with an alligator clip and wire. Fasten the wire to the clip and attach it to the antenna stub. The wire isn't critical for local stations, but for short wave listening, it should be as long as possible. Even in a small apartment, a piece of transformer wire tacked up along the ceiling will facilitate worldwide reception.
Improvise a more elegant antenna by attaching a bulk head mount BNC connector to the radio cover. Remove the cover and drill five holes, one for the center post and four for the mounting screws. Locate the antenna wire and disconnect it from the broken antenna. Solder it to the center post in the BNC connector. Install the cover and attach a flexible antenna (called a "rubber duck" by ham operators). Alternatively, you can use an old coaxial cable with a BNC connector by removing the outer cover and braided sheath.
Antennas have great impact on radio performance, so don't be afraid to tinker with various designs.
Unplug radios before removing protective covers. Be careful that an antenna does not contact live electrical wires.