I pray for his intentions. Are there other things ppl do to show respect?
This is a small technicality, but since you want to be very correct, I’m pointing it out.
Note that praying for the “intentions of the Holy Father” (also called “intentions of the Sovereign Pontiff”) is not the same thing as praying for the Pope personally. I try to get plenary indulgences frequently, and there is a requirement that one recite prayers for the “intentions of the Sovereign Pontiff”. I originally thought this meant you were just praying for the Pope, e.g. “for our Holy Father, Pope Francis, we pray”. A lot of other Catholics think the same thing.
However, for indulgences we must recite the prayers “for the INTENTIONS of our Holy Father” which means a specific set of general intentions, usually listed as something like this (sometimes with slightly different wording)
i. The progress of the Faith and triumph of the Church.
ii. Peace and union among Christian Princes and Rulers.
iii. The conversion of sinners.
iv. The uprooting of heresy.
In addition to these intentions, the Pope adds a specific monthly intention from a list that is made up at the beginning of each year. Here is the list of the Pope’s monthly intentions for 2017:
http://www.usccb.org/prayer-and-worship/prayers-and-devotions/the-popes-monthly-intention.cfm
When you “pray for the Pope’s intentions” you do NOT need to recite the specific intentions or even know/ remember what they are. Just saying “I pray for the Pope’s intentions” and then saying some prayers (they recommend one Our Father and one Hail Mary, but you’re free to say another prayer if you like) is sufficient.
BUT, this is not the same as praying for the person of the Pope, and in fact you can pray “for the Holy Father’s intentions” even when the Holy See is vacant because the Pope just died and they haven’t yet elected a new Pope. (People always ask this question when they are trying to get a plenary indulgence but there doesn’t happen to be a Pope in office.)
If you want to, in addition, pray for the person of the Pope, you would say “I pray for the person of our Pope Francis, may God protect him and guide him” etc. and then say another prayer.
I usually pray for the Pope’s intentions after every Holy Communion saying 1 Our Father, 1 Hail Mary, and 1 Glory Be, and then I say an extra Hail Mary for the person of the Pope. That way I’m covered for the indulgence (by praying for the INTENTIONS) and I have also prayed personally for his PERSON, i.e. the protection of the current Pope in office. If we didn’t have a Pope in office, I would still pray for the INTENTIONS but skip the prayer for his PERSON and pray that God guide the cardinals in selecting a worthy new Pope, and pray for the soul of the recently deceased Pope if one died.
Just thought I’d note the difference so you can pray for both Intentions and Person of the Holy Father.
Here is a good source that explains “intentions of the Holy Father” in some detail. It’s the one that clarified this question for me.