Can I replace a Shimano Deore SL-M590 3speed Left shifter with an Acera SL-M310?
Short answer - yes it will work, its a 3 speed Shimano "mountain" shifter so the amount of cable pull should be identical. 

Long answer - You get what you pay for. 

Acera is the cheapest of the M series groupsets. Above it you have Alivio , then Deore. In saying that, Shimano's trickle down development tends to send improvements down the production line over the years so a 2018 Acera won't be much worse than a 2009 Deore. 

You won't (initially) notice much difference in shifting quality. It'll probably feel better for a while.

Yes it will be plasticky. yes it will break faster than a new Deore part. YMMV depending on what sort of riding you do.

You can find many tutorials on YouTube on how to do this ("replace front shifter bike"). With luck you just need a 4mm and 5mm Hex and to be able to get the left grip off. Worse luck, the cable housing has degraded and needs replacing too.