Q: Why is 1 carbon not bonded to any hydrogens?
Ans: Valency. Each carbon atom can only bond to a maximum of 4 Atoms. There's no room for hydrogens.
The horizontal line is the carbon chain. The vertical line is the branches that stem off the carbon chain.
This molecule is quite complex to start off with, but essentially the longest out of the horizontal/vertical chain is the carbon back bone of the molecule .
In this case the horizontal line is the largest, hence the molecule is a butane compound.
The shortest is the vertical line that has two methyl groups attached on the 2nd Butane carbon.
Hence, you'd call it
.. 2-dimethylbutane