Assume I have found and want to eat a to me unknown kind of mushroom. Is there some way to find out if that mushroom is poisonous by looking/smelling/soaking it?
No as per: "There are no outward characteristics that all poisonous mushrooms have in common, so picking and eating wild mushrooms requires the utmost caution. To be absolutely safe, the only mushrooms you should eat are those found at supermarkets and restaurants!
All the old wives’ tales about how to tell if a mushroom is poisonous – such as whether it tarnishes silverware or turns blue when bruised – are dead wrong.
There’s a saying that there’s no such thing as an old, bold mushroom hunter."
There's a process in the US Army Survival manual on how to determine which plants are suitable for eating and/or hygiene purposes, but even it states:
Do not eat mushrooms in a survival situation! The only way to tell if a mushroom is edible is by positive identification. There is no room for experimentation. Symptoms of the most dangerous mushrooms affecting the central nervous system may show up after several days have passed when it is too late to reverse their effects.
You cannot tell, and there is no specific single method.
This is definitely one of those things that cannot just be described on a Q&A site like this.
Start studying, without eating.
Find an expert and train your eyes and other senses.
Graduate to gathering and have someone else confirm your identification prior to cooking.
Even those experts do sometimes make mistakes, there are just so many kinds of fungi.
As my Scout-master used to say "You can eat any mushroom you want. At least once..."
Good Luck - be careful
The only way to know if a mushroom is poisonous is to have a mushrooms book, or (better) to be an expert.
There are some methods that allow you to distinguish two similar mushrooms, but there isn't a method to know if a mushroom is poisonous/toxic.
There is no general rule for all poisonous or non-poisonous mushrooms. The way you tell is you learn what each particular edible mushroom looks like, and how to tell it apart from any and all similar-looking poisonous mushrooms. If you're unsure of your identification, you don't eat it. Basically, you assume a mushroom is guilty until proven innocent, never the other way round.
It's not a skill that's impossible to learn - people have been gathering mushrooms for centuries, and still are. But it is a skill that takes a lot of practice. And it is better learnt with an expert, rather than with a book.
In particular, a young mushroom can look quite different from the same mushroom when mature, with a poisonous mature mushroom looking similar to an edible young one, for example. You'd need to learn to tell the difference.
Sometimes the surest way to distinguish a poisonous mushroom from its edible cousin is what tree it grows under.
Etc. Some signs are non-trivial. I wouldn't trust my life to "what I learn from a book with OK-ish pictures".
Also note that a mushroom expert would very often be an expert only in their local forests. Edible mushrooms in Europe might have poisonous similar-looking cousins in the US, and vice versa.
Finally, there are mushrooms that are only edible after cooking, as they contain toxins that are destroyed by heat. That's not outlandish - potatoes are the same. But it is yet another thing you need to be aware of.
Feed the unknown mushroom to someone you don't like. After they die and you get put on trial for murder, the prosecutor will put some fancy biologist on the stand to recite some long string of latin sounding words that are the name of the mushroom. Ta-da! You now know the name of the mushroom and that it is poisonous.