The central aspect of the korbanot was the “Olah” (עלה; pl. “Olot”/עלות) — the “burnt offering.”
We can think of them not just as actions, but as expressions of feeling at special times, and for special reasons.
“[The burnt-offering] embodies the idea of the submission of the worshipper to the will of G-d in its most perfect form, as the entire animal was placed upon the Altar to be burnt. [Another] Hebrew name for burnt-offering, olah/עלה, signifies ‘that which ascends’, symbolizing the ascent of the soul in worship. ‘By making the offering ascend to heaven, the one who offers it expresses his desire and intention to ascend himself to Heaven; i.e. to devote himself entirely to G-d and place his life in G-d’s service’.” 
Some general categories might be:
1. Olah Tamid – A communal offering brought twice daily: once in the morning and once in the afternoon. Our “Shachrit” (morning) and “Minchah” (afternoon) services correspond to these. The “Ma’ariv” (evening) service has a different source. In particular, the “Amidah,” or “Sh’monah Esrei” (prayer) represents this offering liturgically. This might also suggest that it’s of maximum spiritual benefit for us to begin and end each day by re-aligning ourselves with G-d.
2. Musaf offerings – Varying numbers of additional korbanot/olot brought as components of the Shabbat, Rosh Chodesh and the Yom Tovim [Festivals] offerings. Our “Musaf” services on Shabbat and holidays correspond to these. The extra offerings suggest added emotional and spiritual intensity. It helps separate ordinary days from days set apart for special holy, spiritual purposes. Having two challot on a Shabbat or holiday might be a reminder of this, too. What personal things do you do to distinguish Shabbat or holidays from your daily life?
3. An obligatory personal Olah…in certain specific situations. These include a woman after childbirth, a metzora, a nazir, a convert, and a person who visits the Temple on the three festivals. These might be associated with returning from some change in your life that had temporarily modified or prevented your worshipping with the community. It’s a kind of “re-union” offering.
4. A voluntarily Olah brought by an individual as an offering. This corresponds to the personal, voluntary things we do to feel closer to G-d — reciting Psalms (Tehillim), for example; perhaps meditating would fall in this category, too. Voluntary Torah-study could be in this category. Sometimes, even when we say prayers that are written for us, or do other things that are a regular part of “religious” life, we feel the need to do something extra, of our own, to give ourselves a revived sense of G-d’s closeness to us.
5. Communal Olot offered by the Kohanim when no other Korban was being processed. This was done to maintain the spiritual quality of the place where offerings were done, even when none were being done actively. This would relate to things we might do to keep a synagogue feeling “holy,” even when no service is being done. We not only treat the place as holy, we treat people with special respect while we’re there. We should keep our conversation polite, respectful and most of all — related to the spiritual purpose of the synagogue. If we do, we’ll feel the holiness all the more when we are in fact there for services. 
Another way of categorizing the sacrifices: “These sacrifices can generally be divided into three types: Olah, in which the sacrificed animal is burned entirely on the altar, reflecting a solemn commitment and deference to the Divine; Shlamim, which is mainly brought during personal celebrations and holidays, partly burned, and partly eaten by both the priests and the owner to express the joy of the occasion; and Hatat, brought as an atonement for sin and partly burned and partly eaten by the priests but not by the owner.” 
An individual or community could bring a korban/olah in response to a special sense of distress. Worshipping G-d at those moments helped people face the intense difficulties more calmly.
This post is, of course, no more than a cursory review of the different types of korbanot. One need only look online at different articles and their illustrative tables about this topic (not to mention those in publications), to see how complicated a discussion of it can become. But for now, a brief overview should suffice.
In these difficult, painful days, is there a way for you to offer your own personal korban, to face what we must more calmly?
(Next post: Steps in doing a “Korban.”)