Download harpo's reference files if you don't have them already. Search this forum for the links.
If you only have regular sins, copy the entire "sins" folder from the reference files, and rename it to your mod name (at least I hope that works, I have Diplomacy myself)
If you have Diplomacy/Entrenchment create an empty mod folder, then copy the following files from the vanilla sins reference files GameInfo folder, place the files in the GameInfo folder of your mod:
RESEARCHSUBJECT_MAXCAPITALSHIPSPHASE0.entity
RESEARCHSUBJECT_MAXCAPITALSHIPSPSI0.entity
RESEARCHSUBJECT_MAXCAPITALSHIPSTECH0.entity
The ones numbered 1 through 7 are the later researches, the ones numbered 0 are the first research, but also set the startup supply.
Open each of these files with a text editor. Find the line " modifierType "CapitalShipMaxSlots" ", then set the "baseValue" to what you want each race to start with. Set the "perLevelValue" in each of the .entity files to what you want a player to gain from that research.
For fleet supply, find
RESEARCHSUBJECT_MAXSHIPSLOTSPHASE0.entity
RESEARCHSUBJECT_MAXSHIPSLOTSPSI0.entity
RESEARCHSUBJECT_MAXSHIPSLOTSTECH0.entity
And edit the line " modifierType "ShipMaxSlots" ", again, "baseValue" is starting supply, "perLevelValue" is supply gained from research.
Then, if you have Entrenchment/Diplomacy copy the entity.manifest from your Entrenchment/Diplomacy installation folder to your mod folder, and you're done.
Note that "PHASE" is the global reference for Vasari, "PSI" for Advent and "TECH" for TEC. Use this to identify files for future mods (though note that not all files use such an index, for example most researches)
Try it even if Shmily123 is kind enough to do it for you, as this is a very basic mod, and a good practice for future work.