Depends on the saint, depends on the culture, depends on how traditional the parish can be.
Obviously the heavens are populated with hundreds if not thousands of saints already so it would be impractical to observe them all but there are big saints that are eternally commemorated - not everyone knows St. Ceolfraed but most people know St. John the Baptist or St. Mary Magdalene.
Depending on the culture, it's customary to have a little festival or engage in recreational activities that remind us of the saint. On the feast of St. John the Baptist's beheading, I like to go swimming since it's usually warm enough outside. In the Philippines, the feast of San Juan Bautista is celebrated with city-wide water-festivals in all the major cities! It is literally impossible to leave your house that day without getting soaking wet. In other European cultures, since Jesus called St. John the Baptist a bright and burning light, bonfires on the night were often built, blessed and then old sacramentals were piously disposed of by throwing them into that fire. Other cultures may eat chocolate insects in order to commemorate St. John who lived off of locusts and honey.
In addition, there's the devotional aspect to it. There are many prayers to the saints: prayers that they composed themselves, novenas that can be said to them leading up to their feast day. If you have an icon or a statue of them at home and a home censer, you can offer up incense, light a candle and pray to them.
There are also many traditional things that parishes can do together as a whole but which are often forgotten, particularly in the Post-VII era. St. Blaise for example was normally associated with a blessing of throats using two blessed candles. Some Marian feasts were celebrated by bringing flowers, seeds and fruits to the parish to have them blessed - since she is the Rod of Jesse from which the Flower of salvation sprung. Then there are also random cool things like looking out for the yearly phenomenon of St. Lawrence's Tears around the feast day of St. Lawrence. I've never seen it but I've known people who have seen falling stars around his feast day - his "tears", since he suffered a particularly gruesome martyrdom. These are only just a few examples!
The sanctification of time is something liturgical Christians do best and 2,000 years of Catholic history has given us a rich patrimony and heritage to remember the heroes of our Chuch. Let's not forget!
EDIT I suppose that having public festivals or even just a large enough parish gathering to be able to celebrate many of these customs would depend on whether we were living in a predominantly Catholic country or not. I suppose in countries where evangelisation and missionary work is more necessary (the USA), it would be more beneficial for Catholics to gather around monasteries to experience this deepening of faith and en-rooting of Catholic culture but this itself may impede the actual evangelisation and missionary work. In countries where more profound catechesis is the emphasis (countries that are already traditionally Catholic), I think these customs would be most beneficial.