The first step we should take in solving this problem is formatting it neatly. From how you wrote it, we can format it as so:
3 + -4 - 8 -(-1) - 1
I would also add addition sign between the numbers
3 + -4 + -8 + -(-1) + -1
Now why the addition signs? In Algebra, it's best to think that you don't really subtract. You ADD NEGATIVE NUMBERS. This will make this problem easier(especially with the next step).
The next step would be to simplify some of these numbers. One I see is -(-1)- see how the addition signs make these easier to simplify? Now, how would we simplify that? One tip is to read this as "the opposite of the opposite of 1". The opposite of one is, of course, -1. But what is the opposite of that? We can figure that out with another tip- if a number has an EVEN amount of negative signs, it will be positive. If there are an odd amount, it will be negative. There are two negative signs; therefore, it will become +1! Now we have the equation:
3 + -4 + -8 + 1 +-1
From here it gets simple. Since everything is addition from here on out, we can just add from left to right(there is no order of operations to worry about since it's all addition). If you need help adding negative numbers, check out this Khanacademy viedo: https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-sub-neg-intro/v/adding-and-subtracting-negative-number-examples.
Now that we can add, let's do that! Let's first do 3 + -4(which is -1)
-1 + -8 +1 +-1
Now we can add -1 and -8(this equals -9)
-9 + 1 + -1
Now let's add 1 and -1(this equals 0)
Now we can see that our answer is -9.
We can check with the calculator: 3+-4-8--1-1 = -9
We are right! Hopefully this step-by-step answer is helpful!