Let me give what comes off the top of my head.

Equipment:
The most important part of your arsenal, you will generally be carrying three pieces of equipment, so that's what I will assume in this scenario. In a random game, I find a revive tool, drop uplinks, and a nanohive work best for me, mostly because they require little communication between squad mates. In a organized squad/corp battle, a revive tool, repair tool, and a nanohive work best for me, mostly because you can't repair practically anyone without making them wait up for your slow logi *ss, hence you will need a mic in that situation.

Modules:
As a logi, you will have a much larger amount of customization, especially when you get a proto suit, which has four high slots and four low slots. I, however, find a type-1 suit to fit my needs perfectly fine and is cost-effective, so I will just give you my thoughts on 2 and 2 suit. As a logi, I find you will rarely find other logi's that want to repair you, so I find an armor repper is a necessity. Being a logi also means lower survivability, so I equip armor plates, but they aren't necessary. Sticking with my survivability stance, both my high slots are equipped with shield extenders.

Weapons:
Despite being a support unit, you will still use a weapon, and I find the simple AR does just fine on a logi loadout, with simple locus grenades.

My methods:
The first thing of being a logi is many people expect you to revive them. Take a look around, watch for snipers, just be generally cautious if you walk up to a team-mate in need of a revive in the middle of the street, also, don't revive people in the center of a gunfight, it's not fun to be revived and instantly be gunned down. If you carry nanohives, I find placing them next to objectives in skirmish gives them the most usage, though place them out of the way so they aren't destroyed by grenades. Drop uplinks should be placed in hidden areas if you use them, obviously you don't want the enemy to find yours and spawn camp it. Like I said before, repairing people is very difficult if you have to chase after them with it, so unless you are communicating with everyone in your squad, I recommend you don't use one. I wish I knew about active scanners, but you will have to find your own use for them if you are interested. Similarly, I have not dabbled in proximity explosives or remote explosives, so I can't give you any tips for them. Stick with a team-mate, but avoid trying to follow with scouts because they are much too fast to keep pace with. If you stick with a large group, like four or more, be wary of orbital strikes.

Skills:
Mechanics and Shield Operation/Management for survival.
Dropsuit Command, Electronics, and Engineering are a must-have, no matter what suit you use.
Minmatar Logistics Dropsuit obviously
Assault Rifle Operation, because you still need to be able to handle yourself in a fight.
Nanocircuitry, Drop Uplink Deployment, and Repair Systems, depending on what equipment you use.
Any skill required for the modules you choose to put on you suit.

I run my logi with necromancer nanites, gauged nanohives, and a flux repair tool. I also us a tactical AR, and av grenades.

Skill wise, I ranked up my shield upgrades, repair, mechanics, engineering, electronics, nano skill, and of course logi suit.

For the most part I only repair my squadmates in ambush, and repair blues in skirmish. I nanite whomever I can, but my squad always comes first. Other than that just take on your opponents at range, and get used to having really low kill scores. I rarely get about 12 kills a match when I run with my squad.

Good luck.