RP is actually really easy and not something you need to worry about. When the DM is speaking as another character, respond like you're having a conversation. That's it. In a very broad sense, RP in D&D is your ability to have conversations.
Put yourself in this situation: if someone responded to your "Greetings/Well met!/Hello" with "I growl angrily, draw my sword and respond: Your flesh smells like my recent prey" you'd gtfo faster than you knew you were able because you're staring at a serial killer. This is kind of the experience many DMs have with talking to players. If you want to be known, at least by your DM, as a good roleplayer, respond "in character" but in a manner that speaks that you are at least aware of how to be a social creature.
When you're speaking to a barkeep, be friendly, polite, ask for drinks, and don't argue about the few coins he asks for. Gold is free for an adventurer. You're literally only paying in the time that you're going to spend adventuring anyway.
When you're talking to random NPC, don't be rude. In the words of Sheldon's mom: "Because they don't like it."
When you're talking to the King/Queen/Person of Power: Be very polite and respectful. Compliment them for no reason. Don't pester them with stupid questions, don't pry into their personal lives incessantly. You wouldn't do that to your boss at work, because that's a really good way to be written up for harassment.
When you're talking to the obvious bad guy: In character you have no idea of their power, so keeping them talking is an absolutely wonderful way to gauge what they're capable of, learn what they think of themselves, and what their plans are. Give your battle master fighter the time to use their class ability to determine relative power of an enemy. (Personally I'd love it if my players would talk to my bad guys rather than "I shoot him with my bow." This tells me that they're literally not interested in the slightest and only ends up with them having to draw conclusions about what exactly this person was doing there in the first place.)
As a DM I'm actually really not a fan of descriptive RP. I think it's useless and distracting most of the time, so unless it's super relevant that you make a flourish with your cape as you sit down at a table and take a slow sip of your mead, you're literally just wasting everyone's time looking like a nerd. Keep talking like a normal person. It makes the DMs job so much easier and actually nets you WAY more information. It always amazes me how many players will simply default to the rude, abrasive, demanding, uneducated brute to get information when simply buying them a drink and trying to make friends would be so much easier, take less time, and not make enemies. Like, even with unfriendly NPCs, being friendly and polite is very disarming, it's really not that hard to change opinions when you're not being an ass. /rant Sorry... got caught up in that...
Basically, you don't need to have a super complex character, manner of speech, accent, or anything that makes things "hard" or too different. Speak like a normal socialized person but ask relevant questions and don't try to "explore the entire dialogue tree" in every conversation. When it looks like the NPC doesn't like the line of conversation, try to get back into their good graces. Rogues love being bribed. Nobles love being complimented but take slights to their character much more seriously. Being able to navigate different social stratii and taking cues is one of the biggest things to practice.