Hello John!
As the other posters have said, it depends on your budget and your goals. To simplify an incredibly confusing subject, when you first approach it, you basically have four options. I've placed them in increasing order of cost.
1) Use TV speakers
Accept that modern TVs have a great picture but not so great sound and just watch Bananarama videos with the sound turned off.
Cost: zero
2) Powered speakers
The solution that Quaddy mentioned - plug a pair (or trio, if 2.1 - i.e. two main speakers plus a subwoofer) into the headphone socket or the pair of "Audio Out" sockets towards the bottom left of the panel of connections (that's probably better but you may then need to find the setting on your TV for external sound, which will turn off the TV speakers. Plugging into the headphone socket will probably turn off the internal speakers without doing that).
The speakers would need to be powered and amplified - basically, if they have jack or cinch inputs (headphone socket or audio inputs matching the AUDIO OUT sockets on the TV) then they are amplified; if they just have bare wire speakers connection then they aren't.
This will give you better, but not great, sound, limited to stereo.
Cost: minimal, from £20.
3) Stereo amplifier
This is where it starts getting serious, and this is many people's preferred option, particularly if they don't watch action films (which are the most likely to use surround sound) or if they also want to use the speakers for playing music. You get a stereo amplifier and a pair of speakers (unpowered, this time!), connect the AUDIO OUT sockets on your TV to the amplifier and away you go. If you have other sources, such as a DVD player, you can optionally connect those directly to the amplifier instead of going through the TV, and you can also connect a CD player etc. for music.
This will give you good to excellent sound, but no surround sound.
I have this setup on one TV, with a nice amp and speakers (cost together about £1800, including cables), and it sounds great.
Cost: anything from £100 to several thousands! Realistically, you can already get something that will sound pretty good for £2-300.
[Alternatively, if you already have a stereo system, move it to the TV and use
that, at zero cost!]
4) AV Receiver
The ultimate solution is an AV (audio visual) receiver, which is a surround sound amplifier with video processing. The AV receiver basically acts as the hub of all of your sound and video - you connect all of the sources (TV aerial, satellite tuner, DVD/BD player, game console etc) to the AV receiver, and then that sends the sound and video to the (separate) speakers and TV respectively.
Obviously, this costs more than stereo because you have at least 3 times as many speakers (and amplifier circuits). My setup cost me just under £2000 a couple of months ago.
Advantages: gives you full surround sound (anything from 5.1 to 9.2), simplifies connections to the TV, gives you more connectivity options. On the downside, it can be quite complicated and you may find the multiplicity of remote controls very confusing (I do!).
Cost: a basic package, receiver + surround speakers, can be got for £2-300, I believe. From then on, the sky's the limit. Something pretty decent can probably be found for around £500.
I hope this helps. Now you can pick your solution and start narrowing down the options!