user-1: I'm reading papers since hours and still don't get one thing:
A bitcoin transaction is an information like "Bob sends 2 BTC to Alice". This message is signed with Bobs private key and needs to be added to the blockchain that is distributed to every participant. I also got that you need to calculate a Proof of Work to be able to add something to the chain. Or in other words: The other participants won't accept your block without the proof of work.
How does Bob get this proof of work or how does Bobs message went to a person who has such I proof? I can't believe that every person making a transaction needs to calculate it's own proof. Is it really like that? If not: How does Bobs "message" is transmitted to a person who owns such a proof, how can the person make sure that Bobs message is a valid transaction (and not only garbage) and what the motivation for this person to process Bobs message at all?

user85: 
How does Bob get this proof of work or how does Bobs message went to a person who has such I proof?

Bob offers a fee to whoever attaches his transaction to a block with the necessary proof of work. Now Bob wants to get his transaction to someone who can attach it and people who generate proof of work want Bob's transaction so they can get the fee.
When two people each want to communicate with each other, there is no difficulty in arranging that communication. We have the Internet.

I can't believe that every person making a transaction needs to calculate it's own proof. Is it really like that?

No. Those who want to execute transactions offer a fee to those who calculate proof of work. This is a mutually beneficial arrangement.

If not: How does Bobs "message" is transmitted to a person who owns such a proof,

Over the Internet.

how can the person make sure that Bobs message is a valid transaction (and not only garbage)

They just check to make sure whether it follows all the rules, which everyone knows. If so, it's valid. If not, it's invalid.

and what the motivation for this person to process Bobs message at all?

They want to make as much money as possible for the proof of work they provide. So they actively search for the transactions that offer the highest fees to them.

-1: <p>I'm reading papers since hours and still don't get one thing:
A bitcoin transaction is an information like &quot;Bob sends 2 BTC to Alice&quot;. This message is signed with Bobs private key and needs to be added to the blockchain that is distributed to every participant. I also got that you need to calculate a Proof of Work to be able to add something to the chain. Or in other words: The other participants won't accept your block without the proof of work.</p>
<p>How does Bob get this proof of work or how does Bobs message went to a person who has such I proof? I can't believe that every person making a transaction needs to calculate it's own proof. Is it really like that? If not: How does Bobs &quot;message&quot; is transmitted to a person who owns such a proof, how can the person make sure that Bobs message is a valid transaction (and not only garbage) and what the motivation for this person to process Bobs message at all?</p>
 85: <blockquote>
<p>How does Bob get this proof of work or how does Bobs message went to a person who has such I proof?</p>
</blockquote>
<p>Bob offers a fee to whoever attaches his transaction to a block with the necessary proof of work. Now Bob wants to get his transaction to someone who can attach it and people who generate proof of work want Bob's transaction so they can get the fee.</p>
<p>When two people each want to communicate with each other, there is no difficulty in arranging that communication. We have the Internet.</p>
<blockquote>
<p>I can't believe that every person making a transaction needs to calculate it's own proof. Is it really like that?</p>
</blockquote>
<p>No. Those who want to execute transactions offer a fee to those who calculate proof of work. This is a mutually beneficial arrangement.</p>
<blockquote>
<p>If not: How does Bobs &quot;message&quot; is transmitted to a person who owns such a proof,</p>
</blockquote>
<p>Over the Internet.</p>
<blockquote>
<p>how can the person make sure that Bobs message is a valid transaction (and not only garbage)</p>
</blockquote>
<p>They just check to make sure whether it follows all the rules, which everyone knows. If so, it's valid. If not, it's invalid.</p>
<blockquote>
<p>and what the motivation for this person to process Bobs message at all?</p>
</blockquote>
<p>They want to make as much money as possible for the proof of work they provide. So they actively search for the transactions that offer the highest fees to them.</p>
