It's mostly about learning to listen to yourself. Have you ever noticed that your voice sounds weird on a recording? People are often shocked or embarrassed by what their voice actually sounds like. We tend not to pay much attention to the sounds coming out of our mouth, because we're busy concentrating on what we're about to say next. You can't use your voice effectively if you're not really listening to it, so that's what you need to practice first and foremost.
Use the voice recorder app on your phone. Start off by recording whatever comes to mind in your normal speaking voice, then listening back. Describe your day, tell an anecdote, list the contents of your fridge. Do this for a while until you're used to the sound of your own voice. Pay attention to your own speech. How would you describe your accent to a foreigner? Which sounds are most characteristic of your accent? What aspects of your voice are unique?
Listen to a recording of the accent you'd like to learn and practise imitating one short sentence at a time. Record and play back your attempt, listening carefully to each consonant and vowel sound. Hone in on any syllables that sound wrong, comparing the recording you're imitating with the recording of your own attempt. Pay attention to the movements of your mouth and tongue as you speak. Write out sentences phonetically and take notes on the patterns you identify in the accent. If you're particularly dedicated, learn the International Phonetic Alphabet.
Study linguistics. In particular phonology. and practice the different associated sounds. Essentially there are huge differences in how different accents make sounds to say the same words that we take for granted. British English is actually amazingly varied for this in a way American accents aren't. Once you understand how the sound is differently made depending on who says it for the exact same word, you can analyses and imitate it better.
>>6230 I've said this before, but my favourite impressionist moment was Jon Culshaw on the One Show. He was surprising a woman in a call centre by pretending to be Alan Carr. He snuck up behind her for the big reveal and the disappointment on her face when she saw it was him instead of Carr will stick with me for the rest of my life.