Watch movies with actors who have an English, Irish or Japanese accent. Write down various words you notice pronounced differently and practice them. Take note of differing vowel and consonant sounds. Exposure to the accent you desire will help you immerse yourself in the accent.
Enunciate slowly and carefully. Before an accent can become second nature, it will have to be practiced with care. Enunciate every syllable to focus on how each one differs from your American accent. For example, an "er" ending with a British accent may sound more like an "ah" ending in the American accent. Honing-in on these differences will help you pick up the accent quickly.
Talk to others with the accent you are trying to learn. If you have an English friend, talk with him often and pay close attention to the way he forms words. Listen carefully to which words are different from your own American accent, and which ones are fairly similar.
Mimic what you hear. When in conversation with your English, Irish or Japanese friends -- or after carefully listening to accents on TV, try mimicking different phrases until you have the accent mastered. Copy the way someone with the accent moves their mouth and lips to form words.
Think in your accent. Whether it is English, Irish or Japanese, you must start thinking in that accent. After a long time practicing the accent in your head, it will encourage the words to flow more easily and naturally from your mouth.
Record yourself speaking in the accent. The easiest way to determine if you are speaking in a proper English, Irish or Japanese accent is to listen to yourself speak. Pay attention to problem words so you can focus on correcting them in the future.
Practice as much as you can. An accent can only truly be mastered by continuously practicing it. Focus all of your efforts on the accent. The more you practice, the better you will become.