I wrote this guide for my guildies after having to struggle to 5.2k on my own. It's definitely not complete and is written from an Alliance/Lordaeron perspective, but it should be pretty easy to apply this advice to Horde or other servers. Also, if I left something out, please let me know!
1.0 Type /join Global and manually find a group for normal Forge of Souls, Pit of Saron, and Halls of Reflection. The gear that drops here is great and will easily outclass anything you're wearing right now. This will be your first and most rewarding grind, and nothing else really competes with it for now. Keep farming these dungeons until you have good enough gear that the game lets you use the dungeon finder to find groups for heroic dungeons.
2.0 Once you unlock random heroic dungeons, that should be the main way you spend your time. The first one you complete each day gives you two Emblems of Frost which are used to buy raid-level gear, and each dungeon after that gives you two Emblems of Triumph which are used to buy pre-raid gear. Each boss in a heroic dungeon also drops Emblems of Triumph. There are two vendors for Emblems of Triumph: one in Dalaran up the stairs to the right of the portals to Stormwind and other capital cities, and another in the Dalaran shop that sells the appropriate armor class for your character (for example, mages would go to the cloth armor vendor). Collecting a lot of Emblems of Triumph and buying most of the things from these vendors is your next grind, but don't worry if you occasionally feel like your equipment is better than whatever is on sale. Everything else that I list here are things that you can do while you're waiting in queue for Random Heroics
2.1 Raise your professions to 450. You'll need several thousands of gold to buy a couple pieces of endgame gear, and having max professions is one way to make money.
2.2 Complete quests in Icecrown Citadel and the Argent Tournament. These quests give you access to some of the easiest, most closely concentrated daily quests in the game, which are an easy source of money.
2.3 Complete quests in Storm Peaks. There is a faction there called the Sons of Hodir who sell shoulder enchantments that you need in order to be at your strongest. There's a long and fun quest chain that you have to do in order to become friendly with them, starting with They Took Our Men! in K3. You will eventually need to reach exalted with the Sons of Hodir, but that's a long-term goal.
2.4 Earn Exalted reputation with Northrend factions. Each faction sells a different head enchantment, use Gnarly Guides https://www.gnarlyguides.com/wotlk/class-guides/ to see which faction is best suited for your class and spec. Once you earn Friendly reputation with a faction, their quartermaster will sell you a tabard that you can equip to gain reputation for that faction while in level 80 dungeons.
2.5 Weekly Raid Quests, usually Flame Leviathan Must Die!. These give you 5 Emblems of Triump and 5 Emblems of Frost, and are in raids that are quite easy. If you see a group forming and you haven't done it yet, make sure to join up.
3.0 Once your GS is 3.5k or higher, you can take breaks from the Heroic grind by doing a couple other grinds:
3.1 ICC Stairs Rep Grind. This is one of the most boring grinds in the game. You stand still and kill one single mob at a time to earn reputation with the Ashen Verdict, at the entrance to Icecrown Citadel. You get an amazing ring at Friendly reputation, and the ring upgrades with each reputation level, but it takes quite a long time to reach Exalted just by killing the mobs at the stairs.
3.2 ToC5 Normal Trinket farm. Bosses number two and three in normal Trial of the Champion drop trinkets that are very useful for DPS, caster DPS, healer, and tank classes. It's absolutely worth running the instance over and over again to get your trinket, and you'll see groups forming for it all the time.
4.0 You'll eventually get to the point where you don't want to buy anything with Emblems of Triumph. That means you're very close to raiding!
4.1 Make sure to do Heroic FoS, PoS, and HoR each day until you have all of the relevant gear from there for your class. The gear from these heroic dungeons competes with or beats Emblem of Triumph gear.
4.2 If you aren't exalted with the Sons of Hodir yet, trade your leftover Emblems of Triumph in for Sons of Hodir Commendations to help finish the grind.
4.3 Make sure your reputation with the Ashen Verdict is at least Revered, if not Exalted.
4.4 If you are still struggling with a low Gearscore, consider buying bind-on-equip epic gear from other players or crafting it for yourself.
4.5 At this point, you will be wearing your gear for a while. Invest in endgame enchantments and epic gems for your gear, and make sure to advertise yourself as "4.8k GS gemmed and enchanted". Grizzly Guides is a great resource to see what gems and enchants are best for your class, check it out here https://www.gnarlyguides.com/wotlk/class-guides/
IMPORTANT NOTE FOR ACQUIRING GEMS: You can trade 10k honor for 1 uncut epic gem at the Jewlecrafting PvP Vendor in Stormwind City. Doing the weekly Wintergrasp quests and buying commendations with Stone Keeper Shards can get you several gems each week. You can also trade Emblems of Triumph for them in Dalaran at the rate of 10 Emblems for Red/Blue/Yellow and 20 Emblems for Purple/Green/Orange gems. I recommend using Honor for gems and using Emblems for Sons of Hodir rep and Heirloom gear for any alts you might make, but if you don't want to make alts and are maxed on Sons of Hodir rep then this could be a good extra source of income.
5.0 It's raiding time! This part of the guide is still under construction. Raid progression and reasonable gearscore requests for them are listed below. Something to keep in mind is that the popularity of your class and role may influence raid leader's decision whether to accept you. Classes such as healers, warlocks, and shadow priests can expect to find raids at these gear scores fairly easily, but death knights and warriors may have more difficulty. If you're tanking, try to have 100-200 more GS than the numbers listed (or have an overgeared healer).
ICC Stairs Rep Grind doesn't work anymore, as i read in Lorderon's global... Tried it with a fresh lvl80 shaman, and a whole 10man group on one side, and no rep... I cannot find any reference of this "fix" though in the forums.
I think that stairs rep farming was working in retail, so i'd thought that it'd work on warmane... and it did for quite some time.
For people playing on modern Lordaeron - skip the raid section entirely. Almost all pugs on the server won't let you in unless you already have the achievement, and outgear the raid. Average asking for ICC10 in global nowadays is 5.8k to 6k, for ToC10 is 5.5k.
I've even seen people ask for 5.5k+ for *Malygos*.
Pugs really aren't viable on Lordaeron at all unless you're already basically done with gearing in raids. Find a guild.