How to sketch the following discrete time signal $\sum_{k=0}^{n} \delta[n-k]$?
Your signal is:
$$
x[n]  = \sum_{k=0}^n \delta[n - k]
$$
and you're saying you want to sketch it.

Based on your comment, I'm going to assume that 
$$x[-1] = \left . x[n] \right  |_{n=-1} =  \left . (\delta[n] + \delta[n+1]) \right  |_{n=-1} = 0 + 1 = 1$$
and that
$$x[+1] = \left . x[n] \right  |_{n=+1} =  \left . \left(\delta[n] + \delta[n-1]\right) \right  |_{n=+1} = 0 + 1 = 1$$

I believe that means
$$
x[n] = 1, ~~ \forall n \in \mathbb{Z}
$$
because
$$
x[n]   = \cdots + \delta[n - (n-2)] + \delta[n - (n-1)] + \delta[n - n] + \cdots
$$
if summing up or
$$
x[n]   = \cdots + \delta[n - (n+2)] + \delta[n - (n+1)] + \delta[n - n] + \cdots
$$
if summing down.

It's a little odd having the upper limit of the summation depend on the current time and, as I said in the comment, having the summation go down to the upper limit if the upper limit is below the lower one.