An actor worth his salt should have a firm grip over his vocals, strong enough to be able to tweak and modify them as a situation may require. Only when a voice is strong and self-assured does it command attention and respect. Hence, a mastery over voice is a starting point to develop skills leading to good acting accents.
It has been the hallmark of accomplished actors to be able to imitate people hailing from diverse backgrounds with a wide variety of accents. Many renowned actors are known to have started their careers as minor mimicry artists who only rose to the heights of acting later. It is therefore advised to practice regularly and with dedication, so that the tongue becomes familiar with a multitude of accents.
An actor must have an ear that can discern even slight inflections in sounds, absorbing them and then using them to the benefit of her learning. Upon hearing a new accent, a keen learning actor should be able to adopt it in a short time span with minimum effort. This heightened audio sensory awareness can greatly improve her chances, as a successful actor is aware of and proficient in a variety of accents.
Another simple but useful practice is to maintain a chart of various accents that you come across. Entries like "nasal twang" or "guttural sound" or " drawn out vowels" can help develop a repertoire--particularly when practiced regularly. Maintenance of such a chart can reduce confusion and provide clarity about a particular accent that you may face in the future.
The edifice of accent stands on the foundation of confidence. Dearth of confidence may well result in a genuine accent seeming like an adopted one, whereas self-assurance can lead to a secondary accent seeming like an actor's original one. Confidence can thus work wonders in a performance when it comes to delivering different accents.