One big advantage that they have is that you can do a substantial service for various commemorations, and you don’t have to worry too much about how to go about putting them together.
But how do you do an akathist at home? There are more elaborate ways to do it, and simpler ways. You can combine an Akathist with a canon, or several canons. In fact, as part of preparation for communion clergy (and many pious laity) will do three canons and an akathist. The least complicated way to follow that practice is to get the text all laid out, rather than put them together on the fly. Holy Trinity Monastery in Jordanville, NY, publishes
a booklet for this purpose. You can also find that text laid out in their Horologion.
For the complicated order of service for doing an Akathist at home, you can find the outline in the back of the
Jordanville Prayer Book, or
here. However, a simple way to do an akathist is simply to take
the rule of St. Pachomius, and instead of doing the Jesus Prayer 100 times, do the akathist you wish to do at that point.
– Book of Akathists Volume II: To Our Saviour, the Holy Spirit, the Mother of God, and Various Saints
These volumes also have music in the back that works for most of the akathists that are contained in them.
Akathists are especially useful if you are unable to attend services for a feast or the commemoration of a saint, either because of distance, or maybe because your parish has no services for a particular commemoration. There are many akathists that have not been translated into English, and many are being translated all of the time… and new ones are also being composed, and so if you look hard enough, you likely can find an akathist for most major commemorations, and if there isn’t one out now, there may be one in the future.