Darts tuning is meant to determine a setup for your darts that fits your throw. When I am talking about setup I mean the flight/shaft system of the dart. This system is responsible for the aerodynamic behavior of your darts. It must meet the requirements of darts physics (see the technics section for a closer look at this). The main parameter for determining the correct flight/shaft system for you is the angle at which the dart sticks in the board. Unfortunately you can only see this angle when you are playing on a steel tip board. If you are playing only soft tip then you should switch to a steel board for darts tuning.
The correct angle is within 10 to 60 degrees. Just like in the picture above. The more consistent this angle is, the better. For instance, if every dart of your 3 dart series sticks in a different angle then something is wrong. Most likely does your dart wobble considerably, which can only be reduced by serious practicing. However, using a bigger flight shape will also help here as it adds stability.
Generally, bigger flights ("standard" shape or bigger) will give a greater angle, while smaller flights (such as "pear" shape) will give smaller angles. Note that when you are doing darts tuning always use the same shaft for comparison between flight shapes. Shaft length and shaft material have a strong effect on the flight/shaft system.
Also note that shaft weight (or even flight weight!) also have influence on this angle. The heavier the shaft or flight is, the smaller the angle will be. This is important when you decide whether you will use nylon or the heavier aluminum or titan shafts. The shaft rings can also influence this, as they make the shaft heavier.
Darts tuning needs work and patience. It should be done over a couple of days to eliminate possible daily variances in your throw. A good starting setup for darts tuning is middle length nylon shafts with "standard" size flights. From this initial setup you can continue working, depending on whether your angle is too big or too small.
Spinning means that your dart rotates (spins) when you throw it. Some players that have noticed this spin are concerned whether this is okay or a bad thing.
I don't think that spin is a bad thing. It is an additional source for errors, as it is an additional movement, but on the other hand spin also adds stability. In my point of view these two things eliminate each other, so there is no use worrying about it. In no case should you try to consciously make your darts spin or consciously try to eliminate spin.
Spinning has nothing to do with darts tuning. It is not determined or influenced by the flight/shaft system. It is determined by your personal throw.