Do not expect an airline to sell all seats on the plane for the cheapest fare. There could be just a few seats or more depending on an aircraft or route. For certain days of the week (for example, weekends) or during special events and holidays the cheapest fare may not be available at all.
There are high seasons (summer, Christmas etc.) when all fares become more expensive, so it is important to choose the date of departure in a low season as this date determines the season of the fare. That means that you can travel outbound in spring and inbound in summer but still pay the low fare of the spring season for the whole ticket.
Buy tickets in advance but not too early as cheap fares sometimes may not be available 7-8 months in advance (flights appear in reservation systems only 9 months ahead). Good practice is to buy tickets 2-4 months before departure. Some low fares have advance purchase limitations which means that you can get such fare only if you buy a ticket, for example, 21, 14 or 7 days advance.