While @Hardly's answer is correct I believe a bit more information would help.
The order in which transactions appear in a block is up to the miners. So whoever wins the mining game for that block decides which transactions appear in the block and in which order. There is no certain way to affect this behaviour - increasing your transaction's gas price will probably mean it gets added faster in a block (probably even before another transaction which is waiting) but there's no guarantee.
So, as Hardly said, the transactions will be processed in sequence. They are not processed in parallel. So if the two transactions try to perform conflicting actions (such as both sending the full balance of an address elsewhere) the first one to be mined and included in a block wins and the other one gets reverted.
All transactions in a mined block are always guaranteed to be valid and they do not contradict each other.