How to trigger a relay and LED when a certain threshold of 0.15 volts is passed
simulate this circuit &ndash; Schematic created using CircuitLab

So in the schematic i've drawn, you get the behaviour you have requested. 

From left to right:
Input signal (0 - 6V) goes through R1 as a current-limiter, and is clamped to 5V maximum by a 5V Zener diode D1. This is useful to protect the input of your op-amp/comparator. The resistor R6 next to the zener diode ensures the signal input will be pulled low if it floats and will stop strange behaviour on the output relay etc. The protected signal then goes into the non-inverting input of a general purpose op-amp which is in an "open loop" or basically "comparator" mode, where if:

A (non-inverting "+" input) > B (inverting, "-" input) , OUTPUT = HIGH (~5V)

If A &lt; B, then OUTPUT = LOW (~0V).

I have a voltage divider made from Supply A's voltage level, to give 0.15V from 5V through the divider (10k and 310Ohm). This is a "reference" voltage that lets us trigger the logic change at above or below 0.15V. 

The op-amp is a general purpose, single-supply op-amp which will work fine in this diagram as shown. The supply capacitor C1 for it is important, for any IC you use - always have this as close as you can to the VCC and GND pins. 

The output of the op-amp has a pull-down resistor to give it a load, and a discharge path for the MOSFET M1's gate if for some reason the MCP6001 goes high-impedence. It may be removed if you don't want it.

The output of the op-amp then goes to the gate of N-channel MOSFET "M1". This mosfet acts as a "power switch", in a "low side" configuration. This means that the power switch completes the connection of the "Load" to "ground", to allow current to flow. The load is the relay coil (L1) (with protection diode D2) and the LED with a series resistor to limit the LED current. if it's a red LED using only 1.2V and with a 5V supply, to limit the current to 10mA the resistor should be around 330 or 470 Ohms.

The part used in this first circuit is not really what you wanted, but actually the MCP6001 op-amp is probably better than the LM339 comparator for a newbie to start with, because the LM339 uses an open-drain output logic which is annoying because it inverts the logic, whereas the MCP6001 uses a standard 'push-pull' style output which is easier to understand what a logic HIGH and LOW is. You can simply use a P-channel MOSFET (or PNP BJT) for the LM339 though and a different way of using the resistor R4, i'll show that version below:







simulate this circuit

This second version with an open-drain comparator like the LM339 uses a P-channel MOSFET arranged as a "high side switch". This connects the load to the positive power supply (B), and ground in this case is always connected unlike in the last circuit. The high side switch is actually preferable for many more types of loads than a low-side switch, just because some loads do not enjoy having their ground removed, but basically any circuit is fine with the positive power supply rail being removed (switched off).