user33096: I know that the blockchain technology works so well, because everybody has basically a copy of the last ledger.
Therefore, if a transaction happens, everybody inside the network has to "approve" the transaction to do it.
These other participants are then seen as trusted sources.
However, what makes them into trusted sources? Let's say there are only three participants, two make a transaction and one has to decide if the transaction is acceptable or not (does the clearing). What makes him a trusted source?
Are these thoughts right or where am I wrong?
I appreciate your replies!

user5406: 
everybody inside the network has to "approve" the transaction to do it.

I think "approve" is not the best choice of words. They only check whether a transaction is valid or not, no approval is necessary.
To explain with your example with three participants: 
Alice, Bob, and Charlie each have a copy of the blockchain. Alice wants to send bitcoins to Bob.
Two conditions apply:

Alice has to have sufficient bitcoins to fund the transaction.  
The transaction has to have a valid signature.

When Alice broadcasts her transaction, everyone (Alice, Bob and Charlie) can check whether the money is available, because the transaction specifies which coins are being spent.
Also, everyone can check whether the signature is valid because it can only be produced by the owner of said bitcoins. Each user by themselves will immediately dismiss a transaction if the signature is invalid or when there are insufficient funds. 
Next, whenever anyone mines a block, it will include a set of valid transactions to confirm them. When found, the block is broadcasted to the network. Everyone checks that the block is valid and that it only contains valid transactions. Since everyone builds the database from the same blockchain, they all end up having the same state in the database, and therefore will be in agreement which balances are available for spending.
In other words, you can trust your own copy of the blockchain, because you checked every piece of it for validity. However, others may not. Yet, nobody else has to trust your copy of the blockchain, because you can send them the pieces so they can build their own and check the work themselves.

user31844: 
I know that the blockchain technologie works so well, because
  everybody has basically a copy of the last ledger.

Yes, every full bitcoin node has a copy of the blockchain (aka ledger).

Therefore, if a transaction happens, everybody inside the network has
  to "approve" the transaction to do it.

Correct, every transaction is propagated to all bitcoin nodes and it is validated by each one of them. Some of those nodes also do mining and they will include this transaction to a block. If they mine the block successfully (before any others mine their blocks successfully) they propagate their block to all the other bitcoin nodes which validate the block and all the transactions within. Thus, transactions are validated a second time.

These other participants are then seen as trusted sources.
However, what makes them to trusted sources. Let`s say there are only
  three participants, two make a transaction and one has to decide if
  the transaction is ok or not(does the clearing). What makes him a
  trusted source?

No one is considered a trusted source. Bitcoin enables trustless transactions. If we have 1000 bitcoin nodes in the network and user A makes a transaction that sends some coins to user B all 1000 bitcoin nodes will validate the transaction. Then, when the mined block is propagated all 1000 nodes will validate it again. Note, that users A and B may or may not run a full bitcoin node themselves.
Hopefully, that clarifies things a bit.

33096: <p>I know that the blockchain technology works so well, because everybody has basically a copy of the last ledger.</p>
<p>Therefore, if a transaction happens, everybody inside the network has to &quot;approve&quot; the transaction to do it.</p>
<p>These other participants are then seen as trusted sources.</p>
<p>However, what makes them into trusted sources? Let's say there are only three participants, two make a transaction and one has to decide if the transaction is acceptable or not (does the clearing). What makes him a trusted source?</p>
<p>Are these thoughts right or where am I wrong?</p>
<p>I appreciate your replies!</p>
 5406: <blockquote>
  <p>everybody inside the network has to "approve" the transaction to do it.</p>
</blockquote>

<p>I think "approve" is not the best choice of words. They only check whether a transaction is valid or not, no approval is necessary.</p>

<p>To explain with your example with three participants: </p>

<p>Alice, Bob, and Charlie each have a copy of the blockchain. Alice wants to send bitcoins to Bob.<br>
Two conditions apply:</p>

<ul>
<li>Alice has to have sufficient bitcoins to fund the transaction.  </li>
<li>The transaction has to have a valid signature.</li>
</ul>

<p>When Alice broadcasts her transaction, everyone (Alice, Bob and Charlie) can check whether the money is available, because the transaction specifies which coins are being spent.<br>
Also, everyone can check whether the signature is valid because it can only be produced by the owner of said bitcoins. Each user by themselves will immediately dismiss a transaction if the signature is invalid or when there are insufficient funds. </p>

<p>Next, whenever anyone mines a block, it will include a set of valid transactions to confirm them. When found, the block is broadcasted to the network. Everyone checks that the block is valid and that it only contains valid transactions. Since everyone builds the database from the same blockchain, they all end up having the same state in the database, and therefore will be in agreement which balances are available for spending.</p>

<p><strong>In other words, you can trust your own copy of the blockchain, because you checked every piece of it for validity.</strong> However, others may not. Yet, nobody else has to trust your copy of the blockchain, because you can send them the pieces so they can build their own and check the work themselves.</p>
 31844: <blockquote>
  <p>I know that the blockchain technologie works so well, because
  everybody has basically a copy of the last ledger.</p>
</blockquote>

<p>Yes, every full bitcoin node has a copy of the blockchain (aka ledger).</p>

<blockquote>
  <p>Therefore, if a transaction happens, everybody inside the network has
  to "approve" the transaction to do it.</p>
</blockquote>

<p>Correct, every transaction is propagated to all bitcoin nodes and it is validated by each one of them. Some of those nodes also do mining and they will include this transaction to a block. If they mine the block successfully (before any others mine their blocks successfully) they propagate their block to all the other bitcoin nodes which validate the block and all the transactions within. Thus, transactions are validated a second time.</p>

<blockquote>
  <p>These other participants are then seen as trusted sources.</p>
  
  <p>However, what makes them to trusted sources. Let`s say there are only
  three participants, two make a transaction and one has to decide if
  the transaction is ok or not(does the clearing). What makes him a
  trusted source?</p>
</blockquote>

<p>No one is considered a trusted source. Bitcoin enables trustless transactions. If we have 1000 bitcoin nodes in the network and user A makes a transaction that sends some coins to user B all 1000 bitcoin nodes will validate the transaction. Then, when the mined block is propagated all 1000 nodes will validate it again. Note, that users A and B may or may not run a full bitcoin node themselves.</p>

<p>Hopefully, that clarifies things a bit.</p>
