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SSRI medications work by increasing the amount of serotonin available at neuron synapses. Since serotonin affects mood (in very complicated ways), having more of it available in the brain allows for improved mood and reduction in symptoms of depression.
Usually one needs a prescription from a GP or a psychiatrist in order to get SSRI medication. Once you have this prescription, you can pick up the medication at a local pharmacy. I don't know how this system works in the UK or if it differs from the way it works in the US, but in the US this is the process.