You raise two questions, how to interpret search results and how best to search.
When you have difficulty interpreting the text that appears in the search results, you should always click through to view the image of the document (directory, yizkor book, etc.) from which the text was extracted. The actual images are usually very clear as to the order of first name vs. last name, but the text snippets are sometimes not because they are unformatted and also can have errors due to the computerized OCR process that is used to convert the images to text. Having said that, most, but definitely not all, directories primarily use the format last name, first name or last name, first initial. Note that many business directories will stick to one format almost all of the time, but still have a small percentage of entries the other way around, because, in business listings with multiple proprietors, they will list only the first proprietor's name using the majority format (e.g., Katz M. and J. Silverberg).
If you want to find someone with a specific given name, there are a few strategies you can try, but keep in mind that most directories typically only list an abbreviation for the given name (a first initial or Abr. for Abraham, for example). Directories that list full given names (even double names) are in the minority and especially valuable. For your example of Golda Silverberg, here are a few searches you could try:
The quotes will force exact matches to these phrases. You can combine several searches together using | for boolean OR, like this:
"Silverberg Golda" | "Golda Silverberg"
You can also combine the first name, last name and last name, first name searches like this:
since ~n just means find these words with at most n extra words in between, regardless of order (n=2 here, so this would find Golda Charna Silverberg, too).
For this specific surname, you'll probably not want to search for Silverberg, but actually for Silberberg or Zylberberg, if you're looking for people in Poland or Galicia. You could combine searches like this:
"Zylberberg G"~2 | "Silberberg G"~2 | "Zylberberg Golda"~2 | "Silberberg Golda"~2
You don't have to combine the searches, of course, and could do them separately if you find that makes it easier to review the results. (If you are only searching by surname, you can use the D-M Soundex search method to try some spelling variants of the surname, but it does not always place nicely with searches that include both surnames and give names, and, definitely not with searches that include initials.)
Also, when searching for a specific given name, you'll want to think about variants. Might Golda be listed as Zlate?
Finally, and this is very important, some directories, usually telephone directories, contain sections that list multiple people with the same surname, line-after-line, but they only list the surname for the first entry. Subsequent entries have a ditto mark or nothing in place of the surname, and just list the given names, like:
In situations like this, none of the above searches will work. You'll only find the entry by examining all the pages that list Silverberg (or Silberberg or Zylberberg). So, take care not to miss entries in telephone directories because of overly restrictive searches.
My advice generally is to try a search including the given name or first initial, but always due a surname-only search, too. If you are researching a very common surname, though, this might not be feasible.
Probably the most important information for your particular search: women are a lot less likely to be listed in directories than men, so try, if you can, to search for a woman's husband, father, or son, with whom she might be living.