Rule of thumb is to wait until they are at least a year old (older fir larger breeds or those notorious fir orthopaedic issues)
Always have the dog in a harness - it doesn't have to be one sold for canicross but it dies need to be y-shaped at the front and well,fitting round the shoulder- it's important not to inhibit the dog's gait, and not to risk jerking the neck if there are any sudden movements. Fir the same reason you need a bungy lead or one with a good ekasticated section.
It's safer to use a waist lead or attach the lead to a belt/harness you wear - thus means your hands are free and not affecting your gait (injury risk to you, possibility of greater annoyance to the dog by more movement from you). Also if there is an incident you can't drop it and make it worse by the dig being loose.
Make sure you carry water (unless it's only a very short run on a cold day) and offer frequently. Make sure you have somewhere for poo bags and treats (it's another reason why a belt for you is a good idea, all this stuff can go in it).
Let the dog set the pace, stick to soft ground rather than pavement if you can, and avoid steep sections until you know your dog is fit and used to the effort
And have fun! I love running with my little dog. I followed MN advice when we were starting out, and did talk to canicross club members about getting kit that was suitable.
We no longer parkrun, as they have banned elements of safe kit (having dog on waist lead or humans canicross belt/harness - their reasoning being the nonsensical one that some leads are too long, but they're not taking measures to have a maximum length for them!)
Our vet is all for running with dogs, as she says being the right weight and being active are the two most important things in preserving healthy joints.
Have fun!!