It depends on what kind of environment you want to reproduce, but there are two main factors that lead the brain to think a sound is coming from farther away:
- As sound travels through the air, it loses energy, but not evenly across all frequencies. High frequencies are attenuated (become quieter) more quickly than low frequencies. So when we hear a sound that we are familiar with, but with reduced high frequencies, we perceive it as farther away.
- Sounds reflect off of other surfaces and become distorted when they reflect. When a sound source is close to our ears, it is usually much louder than the reflections of that sound. When the source is farther away, it is quieter and therefore the reflections are more audible. The louder the reflections are compared to the direct sound, the farther away a sound will appear to be.
Note that outdoors in an open field, there are pretty much no reflections, so the second bullet point above would not apply. Outdoors in the woods, there are many reflections, but they sound quite different from reflections in a room. Indoors, rooms are usually small enough that the first bullet point doesn't apply very much, and the second one is more important. Once a space is as large as a warehouse or cathedral, there is some noticeable attenuation of high frequencies.
The distorted reflections are called reverberations or reverb for short. So you'll want to use EQ and/or reverb to create depth.
With EQ, I would start with a high shelf filter, drop it down to -6 dB or so, and slowly sweep it down from 20 kHz until I can hear a subtle drop in high frequencies.
With reverb, the easiest thing to do is to set up a decent sounding reverb plugin and adjust the mix (or wet/dry mix) until you find the right balance of direct and reverb sound. A lower mix, or more dry, sounds closer, higher mix or more wet sounds farther away.
If you want to create a better illusion of distance, playing with the pre-delay setting for the reverb can help. The counter-intuitive thing about pre-delay is that a longer setting sounds closer, and a shorter pre-delay sounds farther. Think of pre-delay as being how far the sound source is the from the farthest wall on the other side of the room. A short pre-delay means the sound source is very close to the far wall.
A rough approximation of delay for distance is that 1 ms is approximately 1 foot of distance. So if you make a space that sounds like a warehouse with walls 100 feet away, you might want as much as 100 ms of pre-delay and a mix of 10% or so to make the sound appear very close, and as few as 5 or 10 ms and a mix of around 50% to make the source sound like it's on the other side of the warehouse. Note that mix settings above 50% can give a special effect but don't sound very realistic, unless you can't hear the direct sound at all (like a sound echoing up from the bottom of a canyon).
More details about the meanings of reverb parameters (which can very widely and confusingly) are here:
What do the different reverb parameters mean?