There is something we need to understand: the earth is not heaven and, therefore, suffering is a part of this world. The sooner we accept that, the rest becomes easy because we do not fight suffering but “participate” in it. Christ came to save us through suffering; he did not come to save us from suffering. The throne of Christ, our Lord and King, is the cross. We are but his disciples so how can we expect anything else except but to follow in his footsteps. So, whenever we suffer, God is allowing it because it perfects us. Think of these as opportunities to participate in God’s plan, which, yes, can include suffering. We offer up our suffering when we accept it without complaining. We just continue with the task that needs to be done without having to broadcast it on Twitter or Facebook, or without throwing a silent tantrum against God.
The best time to offer it is during the Mass. The mass is a sacrifice, and when the priest offers the body and blood of Christ to the Father, we become “present” in Christ’s sacrifice to the Father. Remember that God does not experience time linearly the way we do. He is, in fact, present in all moments of time all the time. So in the Eucharistic prayer, when the priest asks him to “remember”, the Father isn’t using his memory to go back to a past event: consider that he is actually is in that event. While this is true for the Father, we are not brought back in time as if we were in a time-machine. In our case, when we remember, we “make present” the sacrifice of Christ in a sacramental way. We shouldn’t worry about not fully understanding this because nobody does. It is a theological “mystery”. That means we can understand parts of it, but never all of it. It does not mean we are irrational. It just means we accept that there are some things we cannot fully understand.
Now here is the key thing to consider. Christ’s ascension into heaven is proof that the Father has accepted his sacrifice on Calvary. So during mass, when the priest offers to the Father the body and blood of Christ, we can place our offering together with that and can be sure that the Father accepts it as well. We piggy-back our own suffering with the suffering of Christ. When the priest raises the body and blood of Christ and says, “Through him, with him, and in him, all glory and honor are yours now and forever,” you can silently say something like, “Lord, I offer to you all the sufferings I endured this week.” And don’t forget to say, “Amen” at the end of the priest’s prayer because you are acknowledging that you agree with the priest praying for you. This is called the “big amen” and legend has it that the early Christians would say this so loud that it would “rock pagan temples.” (This, of course, is a hyperbole, and it drives the point of its importance.)
It actually would be a good idea to collect yourself a few minutes before the mass and recall all the things you want to offer. They don’t need to be only sufferings. You can offer your joys, too. You can offer your work. You can offer yourself. (Subjects in a kingdom offer themselves and their work to the king.) When you do this regularly, you will develop the habit of thinking that your suffering, your work, and your menial tasks won’t be meaningless because they are going somewhere good – they are going to God.