Much the same as now, mostly, I think.
Modern antidepressants like SSRIs (e.g. sertraline, citalopram, fluoxetine etc.) have an NNT or "number needed to treat" in depression of about 7, which means that you need to give the antidepressants to 7 depressed people in order for one person to benefit. The other six, some of them will get better through the placebo effect, some will get better on their own, and some won't get better at all. Other classes of antidepressants (SNRIs, TCAs, MAOIs, others) have similar NNTs. Antidepressants just aren't that effective, even though they're on a par with many drugs for physical conditions.
So I suppose that like now, many people got on with life despite feeling like shit if they were able to, relied on family to support them, turned to alcohol or recreational drugs, killed themselves, made life or lifestyle changes (radical or otherwise), were unable to cope and sank under the pressure becoming homeless or otherwise failing to function, tried traditional remedies, tried remedies that had a placebo effect, tried religious rituals, or tried to change the way they felt by talking to someone — a therapist, a religious mentor, a friend, someone with claimed magical powers, or whoever might fill that role in the society they lived in.
Depending on the period in history there were also different medical or other socially-approved treatments, with different levels of success based either on medical effects, psychosocial mechanisms or placebo effect. Psychiatric hospitals, asylums and institutions for those with severe enough problems or who could pay, physical treatments with electricity and insulin and cold water to try and shock the brain into changing, traditional herbal or other folk remedies (some of which are effective antidepressants), drugs that aren't strictly antidepressants but can help some people with depression, brain surgery, traditional social interventions that work on a family or village level, various things really.
But I suspect mostly it was fairly similar — a lot of people with depression eventually felt better through natural recovery or recovery assisted by non-antidepressant factors, a lot of people just pushed on through their ongoing or recurrent depression, and a few people weren't able to function or ended up dying from it.