It is do-able but it's not as easy as flicking a switch or pressing a button. You'll need to make a fairly substantial investment in hardware. We are talking about £300+ for entry-level gear and possibly more.
In order to do what you want the dialogue has to be on a separate channel to everything else. That only happens if the TV or satellite or cable receiver is getting a properly encoded Dolby Digital signal or the programme you're watching is encoded with Dolby Surround. These are the DD and DS symbols you might sometimes see in the channel guide. There is a way to 'fudge' a centre channel signal from programmes that are broadcast in pure stereo: Audio systems with Dolby Pro-Logic decoders can create a simulated multichannel effect but it will never be as clean as a signal encoded with separate channel information. In effect you'll still hear some of the front channel music and sound effects when using Dolby ProLogic to simulate a multichannel signal from a plain stereo source signal.
The first part of "How to Listen to Dialogue Only" depends very much then on the way each programme is encoded for broadcast. HD channels are more likely to be broadcast in DD but that doesn't always mean there's a pure centre channel with dialogue only.
The next part of the puzzle is how the signal is handled in your home. This is partly to do with the hardware; how it is connected and how the settings are configured.
Most half decent TVs with an optical output will pass the sound from their internal TV tuner 'as is', so a HD channel broadcasting in full 5.1 DD (where there's a dedicated dialogue channel) will pass that sound out to an external audio system. The same occurs with channels broadcast with Dolby Surround (DS). It is then up to the external audio system to decode the signal in to the various channels. It is the same situation where a TV has a HDMI socket that is ARC enabled. All this is fine if you watch Freeview from the TVs internal tuner; but what happens if you watch Sky or Virgin or have a Freeview PVR to record your favourite programmes? That's where your TV drops the ball.
The signal from the Optical or ARC-enabled HDMI socket is often dumbed down to plain stereo for any source connected via a HDMI cable. So it doesn't matter if you have made sure that your Sky subscription includes all the HD channels and you've set it to output 'Dolby D' in the box's set-up menus; the TV trashes the sound signal and you lose the benefit. This means then that you can't safely go via the TV for any audio connections from external sources. This also rules out using most simple soundbars as they lack the sort of external audio inputs necessary to retain the separate channels. This is partly why you can't hear the centre channel with a simple £50-£100-£150 soundbar.
The answer is a surround system based on a surround receiver that has enough of the right kind of inputs to handle all your sound sources, and that has individual speakers for each channel. This
Yamaha YHT1810 is currently one of the cheapest such systems available. It is £350.