The most convenient way to do the move is really to hire a removals company and let them do everything from packing to unpacking for you. But then that could cost you a lot of money. This means that you have to compromise instead.
You can still do more tasks yourself without being too stressed during the whole process. The secret to this is early and proper planning. Once the move is set, you have to plan all the steps right away. Make a timetable as well to ensure you will be right on time for the move.
Sort your things and prepare appropriate packing materials. In order to save money, you can always ask for sturdy boxes from groceries and liquor stores. You can even simply pick some up at the back of their buildings. Free moving boxes are also given out online. As for the rest of the materials, make sure that you compare prices first so you can get the best deals. Again start packing early so you will not be hurried and too stressed as the moving date approaches.
If you are going to travel long distance, it's less hassle and usually more cost effective to hire a moving company to transport your things. But if the travel is not that far, you can do it yourself without too much trouble and end up saving money. Of course, if you have big furniture and delicate items hiring a moving company would still be more ideal. You should also get sufficient insurance for these things. And if your place is not big enough, you should arrange for storage before the moving date too.