What's your go-to technique for cleaning up background noise in a recording without losing the essence of the audio?

Izotope Rx It's the best!! Ozone team here!!

iZotope RX is the best tto target specific frequencies of noise carefully. I find that working in small increments helps keep the essence and warmth of the original recording intact. Finally, a bit of EQ can help refine any remaining background noise while preserving the core elements of the audio

My go-to technique is to start with noise reduction in either Izotope RX or any spectral denoiser. First, I isolate a section of the recording where it's just the background noise (like a few seconds of silence or consistent hum) and use that to create a noise profile. Then, I apply that profile to the whole track, dialing it back just enough so the noise drops out without killing the natural sound of the voice or instruments. After that, I sometimes use a multiband compressor to control any frequencies that got a bit thin or too bright, helping bring back the fullness. And if needed, a little EQ can smooth it out and make sure the main audio still shines through cleanly. The key is subtlety—just enough to clear out the noise without making it sound over-processed!

Noise removal used to start and end with RX, but IzoTope have been left behind by newer, superior software. I own the full, expensive version of RX and some of the niche tools like de-clip, de-click, de-rustle, de-mouth click, de-hum are excellent for these tasks. But for removal of general background noise and reverb, isolation of dialogue and improving the quality of speech, I don't use RX any more. Today for dialogue clean up I use about 8 different tools depending on the task, often a combination of several of these gets it done. 

iZotope RX is pretty much the best option out there, although it's not the only option. There are great plugins and programs available from Brusfri, Nugen Audio, Goyo, Bertom, Waves, and others. Many of these are also cheaper than iZotope, so that is something to consider as well.

My go-to technique for cleaning up background noise is a combo of noise reduction and smart EQ, keeping things natural without killing the vibe of the recording. First, I like to use iZotope RX for noise reduction—it’s a beast for targeting background hums, hisses, or clicks without wrecking the audio quality. I’ll grab a noise profile from a quiet section and then apply the reduction gently, avoiding that weird, hollow sound you get from over-processing.

After that, I use a subtle EQ to clean up any low-end rumble or high-frequency hiss. If there’s still some room noise or reverb hanging around, a light touch of gating or expansion can help tighten things up. But the key is to go easy—clean it up just enough so the background noise isn’t distracting, but leave enough life in the audio so it still feels natural and organic.

For professional results, consider tools like iZotope RX 11, which excels in precise spectral editing. CEDAR Audio, Waves Clarity and De-Verb plugins are great for overall noise removal, while synthetic restoration plugins can rebuild missing frequencies but should be used with care. 

I'm mostly editing dialog so RX 11 is essential for removing unwanted background noise.  Also consider that in some cases a little background noise can add character and a more "real" feel to a recording.  For instance, some auditions I send in to Ad Agencies for Voice Over, I'll leave in a bit of room tone or record  a bit off mic on purpose if they are asking for a "real person" read.  Overly clean audio for a voice can also sound too close to the listener, essentially giving the listener the feeling that the person speaking or singing is too close to their ear.  I see this a lot on YT videos when creators over use the background noise removal tools and it's off putting to the viewer.  A guy speaking in an empty garage, and yet we hear zero reverb, is confusing to the human brain.  

There are different types of noises, there is just background noise or room reflections, and there is audio interference noise, humming or this hissing sound.
It's of course best to tackle the noise at the source. 

You want to do your recordings in a quiet as possible environment, and vocals preferably in a vocal booth.
If you don't have a professional booth, you can record for instance with a mattress up the wall, or a blanket over your head, this video may look silly but actually helps a lot.

Then there's hiss or audio interference. Every microphone or interface produces some noise. Usually the better your gear the least noise is produced. But its good practise to use a grounded power supply, and not have any high voltage electrical equipment close to your interface or microphone. And watch your ventilators! 

Then when you did all this and there's still noise in your recordings you can have a look at plugins, to remove the noise or room ambience.
There are also countless of free online AI tools available now that can reduce noise or reverb for you from your recordings. 
Just google on "Vocal noise removal AI", "Vocal reverb removal AI" and tons of options will present itself. 
Or you can of course hire a professional like myself or some of the other commenters on Fiverr, and have them remove the noise with the best tools, and experience, and get it reduced as much as possible! 

Good luck