Traditionally, there were seven corporeal acts of mercy: to feed the hungry, to give drink to the thirsty, to clothe the naked, to harbor the harborless, to visit the sick, to ransom the captive, and to bury the dead.
There were also seven spiritual acts of mercy: prayer, doctrine, counsel, solace, correction, remission, and support (they are sometimes given different names, depending on how the Latin is translated).
The idea is this. Acts of mercy, or almsdeeds, are ways in which we give out of our own abundance to meet another's needs. The seven corporeal works of mercy are the more famous set, but we clearly have spiritual needs, too, and these are, in fact, more important. Because of this, the spiritual acts of mercy are more important than the corporeal ones. (In some cases, of course, the corporeal need is more immediate: a starving man may need advice or rebuke, but in general you should feed him first.) The most important spiritual need is for help from God; and thus the most important spiritual almsgiving is the gift of prayer.
Besides help from God, we also need human assistance. Such a need may be due to a deficiency or a disorder. We have two sorts of spiritual deficiency: deficiency in the intellect due to not knowing what to do, and deficiency in the will due to some undesired ill that is suffered. The spiritual act of mercy that remedies deficiency in the intellect is doctrine (instruction), if the deficiency is more a matter of what to believe, or counsel (advice), if the deficiency is more a matter of what to decide. If the deficiency is a matter of will, the remedy is solace or consolation (comfort).
If our need is due to some disorder or sin, the gift that is needed depends on what part of the problem is considered. If we are considering the sinning itself, the proper act of mercy is correction (rebuke) of the sinner. If we are considering the person sinned against, the remedy is remission of the sin or pardon (forgiveness) of the sinner. If we are considering the effects of the sin, the remedy is support of the sinner, both by bearing with the sinner himself and by helping the sinner to bear the consequences of the sin.
Now, naturally, one may have acts that mimic any of these but which are not acts of mercy at all. For instance, instruction out of pride is not a work of mercy, even if you happen to be teaching the right things (which is unlikely: the sort of instruction required by mercy is instruction in the most important and vital things, i.e., the things we genuinely need; pride, however, distorts our sense of priorities and therefore is likely to make us misjudge what is really needed). Likewise, it is generally dangerous to rebuke sinners for sins we ourselves are definitely committing; usually the proper act of mercy in such cases is support, and, in cases where correction is genuinely necessary (e.g. failure to recognize the act as sinful), it can only be done with great self-critique and a fair and open admission of one's own failings. Likewise, no one can forgive any sins not committed against themselves. This bears repeating, because people tend to forget this.
Consider the following story. A former Nazi feels immense guilt for his participation in the Holocaust, and sincerely wants to be forgiven. He seeks out a Jew whose parents were killed at Auschwitz and asks for forgiveness. I remember reading once that a story like this was given to two groups, one Jewish and one Christian, along with the question: Should the Jew forgive the man? The Jews, to a man, said he should not; the Christians, shame to say, all said he should. But clearly the most that can be forgiven by the Jew in the story is any harm he, himself, may have suffered from that particular former Nazi's actions. People do not have the right to forgive sins that are not against themselves. And it cannot be required of him that he do this; the reason we Christians are required to do it is not that it's an objective moral necessity but that 1) we, being abundantly supplied by divine mercy, are called to be charitable; and 2) it is part of being Christlike, and thus a key part of our work as a Church. The whole point of almsgiving is that it is freely given, to a genuine need, out of an abundance we legitimately possess. You cannot be merciful by pretending to have authority you do not have, any more than you can be merciful by pretending to have lots of good advice that you don't, or by pretending to give property that you don't own to the poor. So, for all acts of mercy humility is a necessary condition.
Spiritual almsgiving is immensely difficult, and we will all fail to do it properly more often than we will succeed. But God acts mercifully toward us in all these ways: through prayer, in Christ's mediation; through instruction and counsel, in Scripture; through correction, in Law; through remission, in atonement; and through solace and support, in grace. The least we can do is share the goodness about a bit, to the extent we can.