watasi ha tomodati to ryokou ni tuite hanasimasu.

について is a compound particle meaning “about” or “concerning.” When you want to talk about a topic (in this case, 旅行, “travel”), you attach について directly to the noun:
• 旅行について = “about travel.”
It indicates the subject matter of your talk.

The verb 話す (“to speak/talk”) doesn’t take its topic as a direct object. You don’t say 旅行を話す. Instead:
• Use について to show the topic you’re talking about (“talk about X”).
• で would mark a location or context (“at travel” or “by travel”), which doesn’t fit here.

と after 友達 means “with (someone).” So 友達と = “together with a friend(s).”
• 友達に would mean “to a friend” (indirect object) – not correct here.
• 友達で would indicate “as a friend” or location/context – also not what you want.
You can even expand it to 友達と一緒に if you want to emphasize “together.”

は is the topic marker, so 私は = “as for me.” It sets 私 as the topic of the sentence. In Japanese, if the speaker/subject is obvious, you can drop 私は, giving simply:
友達と旅行について話します。
That still means “I will talk with my friend about travel.”

話します is the polite (ます-form) present/future tense. It corresponds to “will talk” or “talks.” To make it casual/plain, switch to the dictionary form 話す:
• Polite: 話します
• Casual/plain: 話す

Japanese is relatively flexible because particles mark each element’s role. You could say:
• 私は友達と旅行について話します。 (standard)
• 友達と旅行について私は話します。 (topic shifted)
• 旅行について友達と話します。 (focus on what you talk about)
As long as you keep the particles (は, と, について) with their nouns, the meaning stays clear.