DISCLAIMER: The following advice has been written down with utmost care and we have tested these methods ourselves; however we deny any liability for any results.
We strongly do not recommend putting plushies into a washing machine as the fur can get matted easily then. We've heard about quite some horror stories where plushies were ruined then, so don't do it. Although most tags say that the plushie can be machine washed, we strictly advise you not to do it.
Our preferred way is using a wet vacuum cleaner (must be able to soak up liquids, a regular one won't do) or carpet cleaner. In the US, there are some green colored models by a brand starting with B... sold that might come handy if you have several plushies.
Use a mild detergent. Some people from the US recommended Woolite, however we have no experiences with that. Avoid dishwashing soap. Try the detergent on a small, inconspicuous area first.
If you have a wet vacuum cleaner, we recommend working with two buckets of water. Plus a sponge and a soft cleaning cloth (no microfiber).
Otherwise, we just recommend washing the plushie by hand in lukewarm water using a mild detergent.
Make sure to wash the detergent completely out before you proceed. Hint: Push the fur and listen closely. If it doesn't crackle anymore like if you pushed into soap foam, the detergent should be out. Otherwise, change the water and repeat the step above.
Put the plushie on a clothes drying rack or similar. Best if you can put the rack outside on a dry day, but keep it out of direct sunlight. While the plushie dries, ocassionally and gently brush the fur with a soft brush or hair brush. Do not put them into the dryer.
On a plushie up to the size of 60cm/24" length, you may leave the stuffing in for a hand wash. However, if you know how to do it, it would be better if you could remove the stuffing and put it back in when you're done. Wash the stuffing separately if needed.
Please note that airbrushed accents will diminish during washing. This is normal, as airbrush on plush must be water-soluble.