Let's first define Musique Concrète as:
Music crafted from the manipulation of recorded sounds.
You can find more in-depth definitions here and here.
Where to start?
Before we can manipulate sounds, we need to record them. Grab a mic and start recording whatever sound you find interesting. Falling stones, water, voices, rain, cars, wood, strings, metals, anything goes.
Here you can be as pedantic as you can or want. If you don't know much about mics and recording, just grab any mic and record without thinking too much about it. If you know a thing or two about recording and mics (or want to learn), you might want to take your time and experiment with different types of mics (condenser, dynamic, ribbon, different diaphragm sizes, etc) and different recording techniques (position, orientation, maybe stereo techniques like X-Y, ORTF, Blumlein, Mid-Side).
If you don't have a mic you can always use sample libraries, videos, songs, any other source of pre-recorded audio. Recording your sounds opens more possibilities of expressiveness and is a lot of fun, so some people avoid using sounds that were not recorded by them.
Now that you have some sounds, you want to manipulate them.
This is how and where it all started. Analogue tape recorders provide us with some options to manipulate sound, like playback direction, speed-pitch, and cut-paste specific parts of the tape into other regions.
There are other not so obvious tools, like using magnets or substances (or whatever you can think of) to physically alter the tape, inducing interesting (and sometimes unpredictable) changes to the sound.
Sound manipulation in digital flavor. The options are somehow similar to the analogue tape recorders, plus whatever extra a specific sampler is provided with. The options include playback direction, speed-pitch, loop, filters, LFOs.
It's useful to know what types of samplers you have available that can achieve whatever you have in mind. If you are not experienced on this area, try to start with something very simple (like Ableton Live's Simpler), then something more complete (like Native Instrument's Battery or Kontakt), then something more exotic (like sampling/playback tools provided by SuperCollider, Reaktor, or Pure Data).
Samplers evolved. Here the recorded sound is divided in many little parts called grains. These grains can be manipulated independently.
One very interesting implication is that we can now manipulate speed and pitch independently. You might know this by "elastic audio", or "time stretching", or whatever proprietary name that specific algorithm received. This is what pitch-correction tools, like Auto-Tune or Melodyne, use.
The array of manipulation options gets pretty big here. From granular panning (where you assign each individual grain a specific space in the mix) to granular clouds (where every grain is modulated in many ways, like pan, pitch, time, timbre, amplitude).
Different granular tools will give you different options. Native Instrument's Absynth has granular options as oscillator, sampler, and effect. More explicit granular manipulation can be found in synthesis environments (SuperCollider, Pure Data, MAX), at the cost of more complexity.
A very low frequency waveform is scanned. The scanning functions turn that slow wave into one with audio frequencies we can hear. A unique feature of scanned synthesis is its emphasis on the performer's control of timbre. Timbre and pitch can be controlled independently.
Some systems will let you use a sample as the scanned waveform. One example is Native Insruments' Skanner, where two oscillators scan a sample. The speed of the scanning is what gives the pitch to the sound, and the timbre is influenced by the sample.
You can find more about Scanned Synthesis here.
Have fun, go crazy with sound manipulation. You'll discover new tools and new techniques as you go on.
One thing I like to do is re-record sounds manipulating the speaker and the environment. Maybe placing the face of the speaker in the floor, while recording whatever gets out of it inside of a wood box. Maybe put something in the speaker's cone, something that will affect it mechanically.
Maybe use a carbon microphone. Maybe manipulate the sound using vinyl (very easy to do in this day without actually creating a physical vinyl using tools like Traktor or Serato). Try stuff with all the mediums available.
Make some music with it
You might want to mix together some of these sounds and modulations, carving something musical. DAWs are the obvious choice here, but I recommend you something non-linear like Ableton Live or Bitwig Studio.
There are no specific musical patterns or styles, and compositions in this idiom are not restricted to the normal musical rules of melody, harmony, rhythm, metre and so on.
Record and manipulate sounds, make music with them.