A further tip is to remember it is possible clearing one blockage can lead to another elsewhere. For example, a blockage at a sink could shift further down the system and meet with other debris in the line, causing overflow at a shower at a lower drainage point. - MitchellMc
The other method you can try - with due care - is to get a kettle of boiling water and pour it into the shower drain, as quickly as it will take it. It will often soften the soap that is usually the catalyst for blocking drains. Soap combines with any hair & other bits (food, etc) that get washed partly through the pipes. As the blob of gunk forms, it makes everything flow ever slower, which in turn causes the soap-gunk build up to worsen.
Again, please take care - it may be just water, but keep respect for it, to avoid it harming you. Leather shoes in the shower recommended. - TedBear
I've been able to clear a drain with some light plunging in cold water followed by a flush of boiling water before, but some heavier blockages may need a specialised drain cleaner. I'd say try the plunger/flush combo first and if that doesn't work I'd hit it with some drain cleaning gel. After pouring the gel down the drain, you wait around 10 - 15 minutes and then flush it with warm water. Just make sure you don't combine these two methods, flushing the drain cleaner with boiling water will end in a bad, bad time. Make sure you wear rubber gloves for all of this. If both of these methods fail, it might be time to call a plumber. - Jackson
Mostly plunging and hot water, and also unscrewing the waste assembly and clearing it. We've also done baking soda, followed by the boiling water, then white vinegar, then more boiling water. - Kermit