How do I go about finding the hexadecimal sum of 9A88 and 4AF6? I know how to find the decimal sum, but have little understanding of how to find the sum of a hexadecimals?

Adding hexadecimals is exactly the same but when adding you need to count up to 16 (or F) instead of $10$.

Example: $55 + 37$. You first add $5$ with $7$ which yields $12 = 1\times10 + 2>10$. This is too big so you write down $2$ and retain $1$ which means $1\times10$ when adding $5+3$.

For hexadecimals, $9A88 + 4AF6$, first $8+6 = 14 = E$.
Then $8+F = 8+15 = 23 = 7+1\times16$ so you write $7$ down and retain $1$ because you went once over $16$.
Then $A + A + 1 = 10 + 10 + 1 = 21 = 5 + 1\times16$ so you write $5$ down and retain $1$.

Do the last one by yourself using the same argumentation as above and tell me what you find as the final answer to check you did it correctly.

Adding in another base is just like having a different number of fingers. Imagine you have $16$ and go ahead with normal addition.

  9 A 8 8
+ 4 A F 6


Rewrite the $A$s and $F$s in decimal to make it clearer.

  09 10 08 08
+ 04 10 15 06


   1  1
09 10 08 08
+ 04 10 15 06
___________
14 05 07 14


Now convert number $10$-$14$ in the result back to numbers.

  E 5 7 E


Thus your answer is E57E.

Or, if you're lazy, you can just search for an online hex calculator.

One possible way is to convert to decimal, do the addition, and then convert back again. Note that this is probably not the recommended way of doing this kind of arithmetic in general, but it can be useful in order to get a feel for the difference between decimal and hexadecimal numbers.

$\text{9A88}_{16} \, = 9 \cdot 16^3 + 10 \cdot 16^2 + 8 \cdot 16^1 + 8 \cdot 16^0 = 39560$
$\text{4AF6}_{16} = 4 \cdot 16^3 + 10 \cdot 16^2 + 15 \cdot 16^1 + 6 \cdot 16^0 = 19190$

$39560 + 19190 = 58750$

Then convert this number to hexadecimal. In order to do this, we need to divide our answer by $16$ to find the least significant numeral (this will be the remainder), then divide the quotient we got in order to find the next-to-least significant numeral, etc.

$58750 = 3671 \cdot 16 + 14 = 3671 \cdot 16 + \text{E}_{16}$
$3671 = 229 \cdot 16 + 7 = 229 \cdot 16 + \text{7}_{16}$
$229 = 14 \cdot 16 + 5 = 14 \cdot 16 + \text{5}_{16}$
$14 = 14 \cdot 1 + 0 = \text{E}_{16}$

Putting these together, we get our answer:

$\text{E57E}_{16}$