The principle of an field index is the same as a card index in a library, say.
A book has 'fields': Title, Author, ISBN, Category (etc).
Suppose the library is arranged by, say, only the author. If you only knew the title of the book, then you would look up the title in an alphabetical listing of the titles, find out who the author is, and then be able to locate the book on the shelves.
This is faster than looking at every book in the library until you find it, but still, if it was a big library, you'd still take longer than if the library was 'broken up' into categories, say. If the libray was quite small, it wouldn't take too long.
So, whether or not an index is efficient or not depends on how much many records there are to search, and on how many fields you are likely to search on.
In the end, you have to test. If the test-time between having index or not is negligible for a sizeable amount of records, it's probably not worth the effort.
Hope that helps a bit.
P.S. In order to get a good idea of how long a test takes, do the same test many times and take the average. There are a lot of factors involved (mysql, server, browser, op.sys, connection ...).