How will I draw the following signal?
A signal $x(t)$ is a function that maps a time instant $t$ to a corresponding value. Thus, the manipulations that you described in your question apply as they would with any other function:


$x(t-1)$ will effect a right shift along the $t$ axis by $1$ unit.
$-\frac{1}{2}$ will effect a downward shift along the $x(t)$ axis by $\frac{1}{2}$ units.


That is, the role of $-\frac{1}{2}$ is to just subtract that value from the signal at all values of $t$.