There are several ways to mix mortars.
In almost all cases the dry components are mixed first, then water is added and mixed in. There are also times when mixes are used dry.
Very popular, but too expensive and bulky for small jobs. Storage is often impractical. Its often cost effective to buy one for a job then resell afterwards.
Always rinse out before the cement sets if you want the machine to last well.
Can be used to break soft bricks down into powder/pieces which can be incoporated into mortars.
Can also be used to break glass into cullet. Add the glass and add a brick. Pick a hard brick rather than a soft one.
Ditto scrap tiles.
Better suited to paints and lime mortar.
Board & Shovel
This is a flat board with raised edges. Mix dry materials, then add water and mix in. The advantage is its not necessary to maintain a ring to prevent water escape, so work can be quicker.
Bucket & Shovel
Don't fill too full, or you won't be able to mix. Half full is comfortable, more soon becomes hard to mix. Some tendency not to mix material at the bottom well.
Fast Bucket Method
For small amounts its faster to toss the bucket than mix with a small shovel. Move the bucket rapidly in a banana ( shaped motion, and the contents will go round and mix very quickly. At 2 tosses a second a batch can be done in 20 seconds once the water is added.
Works best when the bucket is a quarter full or less.
Mix by kneading the mass of mortar through the plastic. Use of pointed or square cornered tools not recommended.
A drum with securely fitting lid can be used as an unpowered cement mixer. Mixing is much easier if you bolt a bar or 2 down the side on the interior, like the paddles in a motorised cement mixer. Turn by hand or roll along the ground to mix.
The drum can be whatever size suits you, so size and cost are typically much less than for a powered mixer. This often makes storage practical.
Very small amounts can be mixed on a mortar board with a trowel.
For really large batches it is possible to make a giant mixer driven by a car engine. These can be scaled up versions of a cement mixer for cement mortars, or a giant version of a food processor for papercrete and similar formulae.