How to connect LED inside a DIY module

It all depends on where in the circuit you want to integrate it. If your point you want to indicate is the output of an opamp, it can directly drive the LED (don't forget to always add a resistor with the LED or it will burn out!). CDxxxx chips or digital outputs in general have a hard time driving the leds, so then a simple transistor 'switch' circuit is needed.

If you can post your circuit schematic, or the relevant part, i could give more specific ideas 😄

In general, to drive a LED you want a 'transistor as a switch' circuit. You just want the transistor to either connect the LED fully to the power source, or not at all. (If you want a LED to have more subtle variations, depending on the height of the voltage for example, you will need more tweaking and the design will be harder)

For the purpose of just acting like a switch, pretty much any transistor will do. Be careful however that there are different 'flavors' of transistors which work different and also have different schematic symbols. My recomendation would be to use a so called BJT NPN transistor, they are easy to get by in through hole. The specific type/brand does not matter too much, these differ mainly in the region between 'completely on' and 'completely off', which is not really relevant when driving an indicator LED.

'BC547' would be a concrete example, '2N2222' as well. But loads of these specific types will act exactly the same, so just pick a cheap, readily available one 😊

If you Google 'transistor as a switch' you should find a ton of suitable circuits with just the transistor, LED, and maybe 1 or 2 resistors.