There are several ways to mix mortars.
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 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.
When used with haired or fibre reinforced mortar mixes these tend to form 'dead mice' on the paddles (clumps of hair).
Hand held paddle mixers for use in drills put a lot of load on a drill. A high power low speed drill should be used. Using these in a cordless drill is not a realistic option.
Its possible to bend some 2mm iron wire into a makeshift paddle mixer if you keep the shaft short and the stirrer narrow. These are only usable for paint mixing though, not mortar.
Board & Shovel
Its not practical to use a plastic sheet instead of the board, the rigidity is needed.
This is a flat board with raised edges. Mix dry materials, then add water and mix in. The advantage over a board is its not necessary to maintain a ring of mixture 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, so the bottom of the mix needs extra attention.
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. Energetic but very quick.
The bucket needs to be a quarter full or less.
Not a good method, but usable when there's really nothing else to hand. A slow way to mix, and prone to pockets of unmixed mortar remaining. Always some risk of holing the bag too.
Mix mostly with a scoop or trowel, avoiding use of sharp, pointed or square cornered tools. To get all the mix incorporated its necessary to at times lie the bag down and lift its base so all the mix drops into a pile further up the bag.
Only practical when the bag is mostly empty, and the mortar mix forms a layer in the bottom of the bag. Mixing is more or less impossible when significant bulk is present in the bag.
A drum with securely fitting lid can be used as an unpowered cement mixer. Bolt a strip of wood or 2 down the side on the interior to make it work properly, like the paddles in a motorised cement mixer. Turn it by hand or roll along the ground to mix.
The drum can be whatever size suits you, so in principle anything from a paint tin upward. Costs are very small compared to a powered cement mixer. Size is of course limited. Small size often makes storage practical.
Very small amounts can be mixed on a hand held mortar board with a trowel. The same ring technique is used as with a full size board.
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.
Only suited to large cement mixing jobs, Papercrete and similar mixtures. Making one is not a trivial exercise. Purchasing an industrial mixer is prohibitive.