First it should be converted so that we solve for y like your standard graphs:
x - y > -1
Subtract x from both sides:
-y > -x - 1
Now we divide by -1. Note that when we divide by a negative, the inequality sign flips as well. Don't let your graph get messed up by a simple oversight.
y < x + 1
Now it looks mostly like a graphing linear equation, right? The thing to keep in mind is that < sign. That means that when you graph it, you use a dashed line instead of a solid line since the value is not equal to the equation (if it were a ≤ sign, then it would be solid to denote the "equals" part).
The other part to note is that since the sign denotes "less than," then that means any value of x below that line works as well, so you need to shade in the part of the graph below the dashed line.
(3, 0) 0 < 3 + 1 true
(0, 0) 0 < 0 + 1 true
(-1, 0) 0 < -1 + 1 false (but that's why we use the dashed line)
(-2, 0) 0 < -2 + 1 false, so it's not a value that works