How do I write a formula that will search a worksheet tab for names in a
particular column (in this case A), pull all corresponding values for each
hit from another column (in this case D), and give me the sum of all values
from column D on a different tab. The tab with all of the raw data may
contain a few hundred entries at any given time so I need the formula to
accommodate for that.

I have used the "COUNTA" and "COUNTIF" formulas to search for values in the
past, but now I need to perform the search and give me the values from a
different column.

Any help would be greatly appreciated.