The US Patent and Trademark Office (USPTO) allows you to file a trademark application online. Most states also have a trademark filing process, so check with the business office for your state to see which office handles the process if you want to start there.
Make sure to search existing trademarks thoroughly before filing, so you don’t waste the filing fee if someone already registered the mark in the product or service category you want. The USPTO has a search function on it’s website for all US registered trademarks.
Consulting a trademark attorney is often the best way to go simply because trademark law can be confusing and they have the resources to do a global search for you and advise you about which product classifications are correct for your use or intended use.