What is the most efficient way to upgrade a portal?

Solution 1:

When you are alone put the highest resonators available right away.

Placing a resonator gives you 125 AP, while upgrading one gives you 65, but only if you're not the owner of the resonator. Upgrading your own resonators will give you exactly nothing, zero, nil. This means that with a friend you'll get more AP by starting with low-level resonators and gradually upgrading them.

Also you have to remember the limits on resonators' deployment that depends on your level.

Anyway you can always check how many AP you get by looking at the log in your scanner.

Solution 2:

Focus on deployment quality (portal durability)

Try to deploy resonators at maximum range 40 m, your scanner circle has exactly 40 m.
*XMP8 falloff range is 35m.
If possible, deploy strongest resonators to inaccessible places, such as buildings, river, etc.

Best tactical deployment

Always deploy two strongest resonators opposite of each other. If you are alone, but you expect an upgrade soon, place your strongest resonators opposite of each other, but shift the second one 1 slot. This way, you will leave still relatively resistant portal.
*note: If you are not yet level 8, substitute those levels with your highest available resonators.

alone     with        alone
          1 friend    but you expect an upgrade

  6       6 7 6         . 6       7 6 6         6 .
8 - 7     8 - 8       8 - .   >>  8 - 8    OR   8 - 7
  6       6 7 6         6 7       6 6 7           . 6

Focus on AP

125 AP deploy
65  AP upgrade
+500 AP capture (first resonator)
+250 AP fully deployed (last resonator)

• With a friend
  max AP gain: up to 4740 AP (if you are level 8)
  = 500+8*125+250 = 1750 AP + 46*65 = 1750 + 2990 = 4740 AP
  
  *This is the most AP you can get of it and you will use the same amount of each level's resonators.
  The maximums of resonators per agent are:
  8xR1 -> 8xR2 -> 4xR3 -> 4xR4 -> 2xR5 -> 2xR6 -> 1xR7 -> 1xR8

• Alone
  max AP gain: 1750 AP = 500+8*125+250
  Normally deploy your max lvl resonators, you won't get AP for upgrading your own Rs!

You will get additional 125 AP for deploying a portal mod. Max two mods per 1 agent.

Focus on XM

There was a time in Ingress history, where there were no powercubes yet...

Whenever you increase portal's level, it will produce new XM within a minute or two.
1. Deploy a portal so it stays lvl 1 - (1xR8 or any other resonator*).
2. Wait two minutes.
3. Collect XM and raise the level by deploying additional resonators.
for example: 8 -> 7,6 -> 6 -> 5 -> 5,4,4
4. repeat from step 2
*note that you don't need to fully deploy a portal for it to produce new XM.

Solution 3:

How @Kappei says When you're are alone, just go to "upgrade" and then deploy the highest ones you can deploy. (try to put the highest ones in the point where are more difficult to attack).

Upgrades only give points when you upgrade resonators that aren't yours.

The player who "actives" (first reso) has a plus of points, and the last one (who puts the last reso) has a plus of points to.