There are many dialog boxes in HoMM II. Some of them display images; some of them have questions or two choices. 

The HoMM II source code has a very complicated function called NormalDialog with 10 parameters, which has all these options. 

For your common dialog needs, you can use MessageBox or QuestionBox or InputBox. For a few more common variants, such as displaying a dialog box with one or two images, you can use the functions in the AdvMessageBox Lua module. For common uses that aren't in that module, make a request, and we'll add to that module. But if you really need to do something different, you can use the raw AdvMessageBox function.

If this function doesn't make sense, that's not because you're stupid. It's because this function doesn't make sense.

Thank you to forum user DarkAtom for his help reverse-engineering this function.

Syntax:
AdvancedMessageBox(text, dialogtype, position1, position2, img1type, img1arg, img2type, img2arg, writeOr, a10)

text: A string or a variable that contains a string to be displayed
dialogtype: An integer (will be explained below)
position1 and position2: integers, but I still didn't fully discover them; for now, put -1 for both of them to get a centered window
imgtype and imgarg: The image parameters will be explained below.
writeOr: If you set this to DIALOG_OR (1) then an 'or' text will appear in the middle of the box, between the 2 pictures. If only one picture is used, the 'or' text is displayed on top of it. If anything else is passed for this parameter, the "or" will not be shown.
a10: As for the last parameter, I never found a use for it. Leave this set to 0, just to be safe.

Dialogue types:

• 0 or anything below 0 (DIALOG_EMPTY): A window with no buttons, can't get rid of it
• 1 (DIALOG_OKAY): A window with an OK button
• 2 (DIALOG_YES_NO): A window with Yes/No buttons
• 3: A window with a Cancel button
• 4: A window with no buttons, can get rid of it by clicking anywhere (this is probably for right-clicks)
• 5: Same as 1
• 6: Same as 3
• 7: A window with 2 'Learn' buttons (like in the level-up screen)
• 8: A window with a 'Learn' button on the left and nothing on the right
• 9 and above: Same as 0

Image types:

• -1 (IMAGE_EMPTY): No image
• 0 (IMAGE_WOOD): Wood
• 1 (IMAGE_MERCURY): Mercury
• 2 (IMAGE_ORE): Ore
• 3 (IMAGE_SULFUR): Sulfur
• 4 (IMAGE_CRYSTALS): Crystal
• 5 (IMAGE_GEMS): Gems
• 6 (IMAGE_GOLD): Gold
• 7 (IMAGE_GROUP_ARTIFACTS): Artifact
• 8 (IMAGE_GROUP_SPELLS): Spell
• 9 (IMAGE_GROUP_PLAYERS): Player color
• 10 (IMAGE_LUCK): Good Luck
• 11 (IMAGE_BADLUCK): Bad Luck
• 12 (IMAGE_GOOD_MORALE): Good Morale
• 13 (IMAGE_BAD_MORALE): Bad Morale
• 14 (IMAGE_EXP): Experience
• 15 (IMAGE_GROUP_HERO): Hero Portrait
• 16: Not used (if you use it, game will freeze/crash)
• 17 (IMAGE_GROUP_SECONDARY_SKILLS): Secondary Skill
• 18 (IMAGE_GROUP_UNIT): Creature
• 19-24: Same as -1
• 25 (IMAGE_GROUP_PRIMARY_SKILLS): Primary Skill
• 26+: Same as 16

Image subtypes (the number in the list represents the type for which the subtype applies)

• -1: Put 0 to be safe
• 0: Quantity (if you put 0 it will not show any number)
• 1: Quantity (if you put 0 it will not show any number)
• 2: Quantity (if you put 0 it will not show any number)
• 3: Quantity (if you put 0 it will not show any number)
• 4: Quantity (if you put 0 it will not show any number)
• 5: Quantity (if you put 0 it will not show any number)
• 6: Quantity (if you put 0 it will not show any number)
• 7: Which artifact (use artifact name from the wiki)
• 8: Which spell (use spell name from the wiki)
• 9: Which color (blue-0, green-1, red-2, yellow-3, orange-4, purple-5)
• 10: Doesn't matter
• 11: Doesn't matter
• 12: Doesn't matter
• 13: Doesn't matter
• 14: Quantity (works with negatives as well)
• 15: Which portrait (start from 0, it's the same order as when you scroll through them in the editor)**
• 16: As I said above, game crashes, so don't use it
• 17: Which skill * (look at the asterisk below)
• 18: Which creature (take their ID from \data\creatures.xml)
• 19-24: Put 0 to be safe
• 25: 0-3 (Attack, Defense, Spell Power, Knowledge) (100-103 displays a +1 skill)
• 26+: Don't use it

*count the skills in the order from the wiki starting from 0 and stop at the one desired. Then multiply by 3 to get the basic picture. Add 1 for advanced, or 2 for expert   
**for hero portraits: to display town captains, use 90-95 (knight, barbarian, sorceress, warlock, wizard, necromancer)

One more thing I have to mention: If you choose image type resource (0-6), you can set the subtype as negative and it will show the qty/day thing like from the mines. So if I set it to -6, for example, the message will show 6/day.
UPDATE: If you want to show negative values (like when taking resources), put the subtype -x-100000, where x is the value. So -100050 would show -50. If you put exactly -100000, it shows 100k/day, not -0.

UPDATE II: If you enclose text between curly braces {} then the text becomes golden.

For now (Ironfist 1.3.0), none of the dialog types return anything, so it only makes sense to use types 1/5 and 3/6.

I hope this was helpful, please reply if you find anything incorrect information or if you find something new.