We get this question a lot. It actually used to be pretty easy, as most TV sets had analog audio outputs. At least until a few years ago that is. Now, you need to add at least one gadget in order to make this work. If you have an optical output, usually a little square shaped connection labeled "Digital Out". You also might have what looks like the usual RCA jack type connection as a single round jack, also labeled "Digital Out" or something similar.
For these connections, you need a DAC (Digital to Analog Converter) that has the right connection for your TV. These can be had pretty cheaply at $50 or less. They convert the digital signal to audio that can be connected to the Aux connection on your vintage amplifier. You will probably need to go into the TV menu to turn off the built in speakers.
If you don't have these connections, you probably have only the HDMI type. This is typical on more basic TVs. You can get a HDMI audio extractor for a modest price on Amazon. If it's your only option, this will work. Again, connect it to the AUX input, or a Tape In connection on your amp or receiver.