The first thing to say is that the Church encourages us to undertake a variety of acts to assist the souls in purgatory. In principle, any good work or prayer can be offered for the dead. How effective they will be depends both on the relative merit of the act and the holiness and dispositions of the person or persons involved in it.
Hierarchy of good works
In reality, however, some actions are inherently more meritorious than others. So, in broad order of the merit of the action:
- the Mass - most priests offer masses specifically for the dead in November and provide envelopes to make the process easy (though I do wish they would be more upfront in saying wht the appropriate minimum offering is. For the record, the diocese of Melbourne is apparently suggesting $20). If you don't live near a priest who does (or you are concerned about the orthodoxy, fervour, etc of your priest, see below), a number of monasteries (such as Flavigny) and other groups allow you to organise masses to be said on behalf of others online (be kind and charitable though - mass stipends from this time of year an important part of a parish priest's income);
- the Office of the Dead. Liturgical prayer is, as a general principle, more efficacious than other forms of prayer;
- the rosary;
- other indulgenced actions. If you are a daily mass goer who regularly goes to confession it isn't that hard to undertake an action that could attract a plenary indulgence every day that can then be applied to the poor souls (by saying the rosary in a Church or half an hour's prayerful Scripture reading/study a day for example). There are also some particular indulgences relating to the dead - in particular, you can potentially gain a plenary indulgence by visiting a cemetery and praying on each day from November 1 to 8;
- other prayers, fasting, almsgiving and so forth, all traditional good works undertaken to assist the dead.
Here's the trick about the efficacy of actions. Even though in theory the order listed above makes some actions more efficacious than others, in practice it isn't that simple!
Our own holiness, the fervour with which we undertake the action, and the disposition and state of the person or persons we undertake the action for all can play a role in how efficacious the work actually turns out to be. Hence the prayers of a saint can have more efficacy than even having a mass said, attested to by the fact that they can work miracles through their prayers; why historically contemplative nuns have been seen as such an important part of the Church.
So what can we do...
Given that most of us likely aren't actually saints yet, and don't know any (or don't know if they know any!), the hierarchy of merit of actions is a useful starting point. And there are things we can do to maximise the effectiveness of our good works.
Take the Mass. The Mass has infinite merit and value in terms of worship, and at one level all masses are equal given that they are offered by Christ our High Priest. But the 'fruits of the mass', including those that can be applied to a specific intention such as the souls in purgatory, depend on man's actions.
The holier the priest, and the more fervently he says mass, the greater the fruits. A congregation of fervently praying, holy nuns is likely to generate a higher level of fruits. The more fitting the mass itself - the vestments, sacred vessels, etc, the greater the fruits. And here is the one we can most directly influence: the strength of intention and holiness of the person who gave the mass stipend almost certainly matters too....
So, we must all strive to be as holy as possible, to undertake our good works with fervour, and commission priests, religious and other holy people to work on our behalf.
But above all, we must do those good works! Apart from having masses offered and visiting a cemetery (under the usual conditions for a plenary indulgence, or otherwise for a partial indulgence), consider trying to gain partial indulgences for works over the next week or two by: