Be sure to check out USPTO's Trademark Basics pages too!
As trademarks are used nationally, searching USPTO's Trademark Search, is the best option (there is also a Global Brand Database). Anyone looking to register a trademark will need to search to make sure it is not too similar to an already registered trademark since this can cause a common rejection - "likelihood of confusion."
Trademark searching can be more difficult for keywords as it is more about searching for names and their phonetic equivalents, but it still employs the same principles in designing a structured search. Consider these options when designing your search:
Here are some guiding principles from USPTO for conducting a "thorough search" - search:
See the example tab for how to do some searching. With how complex these can get, the free training on searching from USPTO as part of their Trademark Basics Bootcamp is highly recommended!

You're finally ready to sell your new flying car that your company has designed here in the USA.  You have a snazzy logo/stylized words that you want to be protected for your flying car (GEMINI CAR,  , named since it's a two-seater).  How would you get started?
, named since it's a two-seater).  How would you get started?
(image: NASA.gov)
Combining all of these together, you might search like this in Trademark Search using regular expressions:
You might also consider marks with the word car as a symbol instead of spelled out with a star or the constellation representation of Gemini...  Lots of options!  See tmsearch.uspto.gov/help for information on regular expressions and lots of search examples.
There are 6 main categories as you go from your brand idea through maintaining your trademark (see details on USPTO's Trademark Process Overview):


**Note: USPTO has developed a new trademark search system which is live as of November 30, 2023. The link to TESS (old system) will automatically route users to the new system and there are some videos available to help you get started.