I'm assuming that your mailbox has been enabled for full-text search. If it hasn't talk to your Notes/Domino administrators about that.
You haven't mentioned what version of Notes you're using. Recent versions completely changed the search syntax to "web style", but give you the option to return to the older "Note style" syntax. I'll give you info on how to do that if you want at the end of this answer. But first I'll describe the Notes-style syntax because that's what I'm familiar with from about 20 years of use.
The Notes-style full text search syntax is very powerful, with lots of features. By default, it always searches for phrases so that's why quotes aren't helping you. If you enter:
it will only find messages with the phrase "four score". It won't find messages with just "four" or just "score". This is unusual these days as most people are used to the style adopted by web search engines, which would interpret this as a search for pages with "four" or "score", which is why Lotus changed the default style.
Now for further fun with Notes style, consider this one:
four score and seven
This will not search for the phrase "four score and seven", because the word "and" is reserved as an logical AND operator. So this will find messages that contain "four score" and also contain "seven". And based on that, you can probably guess what this search does:
four score or seven
This returns messages containing either "four score" or "seven".
There are a lot of other features. Here are some examples:
four score and not seven
Finds messages that contain "four score" but do not contain "seven"
four score paragraph seven
Finds message that contain "four score" and "seven" within the same paragraph.
four score sentence seven
Finds messages that contain "four score" and "seven" within the same sentence.
Finds messages that contain any word beginning with "four". Frequently you don't need to do this, as Notes search will do "stemming" to find word variants with common suffixes or prefixes, but it can come in handy.
"four score and seven"
Finds the exact phrase "four score and seven". The quotation marks tell the search engine that "and" is part of the phrase instead of an operator.
I'm pretty sure that there are equivalents for some of these things in the web query style syntax, but to be honest, I don't know them and I'm not sure if IBM has ever documented it.
To switch to using the classic Notes search syntax go to the File menu and select Preferences > User Preferences, then click on the Basic tab, and scroll through the Additional Options list, and select "Use Notes (not web) query syntax in the view search bar".
Here are a few links with additional information that may be of interest.
Classic full text search syntax