Time.
The first and most traditional method of steeping is “Time”. Leaving the top off the bottle (allowing air to get to it) will steep and improve a juice by itself, this is usually done by placing the opened bottle in a warm dark place for anything from a day or two up to a week, occasionally giving the bottle a squeeze to expel the air in it and replenish it with fresh air. Benefits are naturally steeped and matured juice, disadvantage, the length of time it takes.
Steeping however, in particular the time element, can be reduced by also employing a number of additional methods.
Agitation.
Vigourous shaking, stirring, etc will help, allow time for the air bubbles to rise to the surface and then repeat again (as many times as you can/want).
Water Bath Heating.
Putting the bottle of juice in a warm (not hot) water bath will shorten the time it takes to mature a juice, it firstly thins the liquid and allows interchange and fusion at a molecular level. However, Heat is an enemy of Nicotine, it will degrade the Nic content if too hot. Warm not Hot water is advised.
Microwave.
Another method of heating is a microwave. This acts like above, but also has another action thought to do with increased molecular particle fusion when juice is blasted with microwaves. Once again, Heat is an enemy of Nicotine, so use in short 1 sec bursts to get it warm, not hot. Oh, and take the cap off first.
Using any (or a combination) of the above methods and then allowing time in a warm dark place, will improve any e-liquid considerably.
Other agitation methods have been employed successfully, including placing bottles in a rotating polisher (for polishing gem stones etc), using a vibrating electrical orbital sander, one report of a person wrapping a bottle in cloth and putting it inside the hubcap of his car for the duration of his daily travel.
Ultrasonics.
This method combines Vibration from ultrasonic frequency or pulses of energy, with or without a warm water bath, reports have been very encouraging when using this method, some say reducing 2 weeks of steeping time to a single day.