How do I conect external radio/speakers to my lg 42lh40-ua

There are many options here. Most HDTVs today have analog audio and digital audio output jacks. You can use RCA audio cables or a 3.5mm connector, whichever your HDTV has to connect the analog stereo output of the TV to any number of devices such as a stereo/amp which has speakers attached. You could also connect an FM transmitter to the TV and send the audio wirelessly to a nearby FM radio, boombox, portable etc. Most HDTVs today have a digital audio output, typically optical, which uses a digital audio cable ($15) to connect to a surround sound receiver. You can also connect the stereo analog output jack on the TV to a 2.4GHz transmitter and receiver speaker combo to get wireless audio outside, in a swimming pool and so forth, all around the house using wireless speakers. These setups usually cost around $150 or so. Look for the jack on the TV labeled AUDIO OUT and see if it is the white and red 2 jack ports or the smaller 3.5mm single jack port. Adapter cables are available at Radio Shack for around $10 should you need them. So you see the options are almost endless.