How do you remove the mold and mildew smell from a couch without having it professionally cleaned.?

If the covers are removable then launder them and add 1/3 cup white vinegar to the rinse. Wouldn't hurt to add 1/3 cup bicarb soda to the wash either. Both absorb odours and the white vinegar will kill the spores.

If that is not possible then get a spray bottle and add 1/3 white vinegar and 1/2 water. Spray the couch really well all over. Wipe up any obvious mould and then re spray and allow to dry, in strong sunlight if possible. You can repeat as often as you want, the white vinegar will not harm the fabric, no matter what it is.

Whenever you have a mold and mildew smell inside your home it is part of an overall Indoor Air Quality (IAQ) issue. Indoor Air Quality is always improved by increasing ventilation which allows fresh air to pass the couch and gives a way for the mildew smell to leave your home,

You can't.