Wrath has been out about 7 or 8 months now. Some players are just now reaching level 80. Whether it’s an alt, or someone who is new to the game, it can be rough on these fresh 80s, especially if they are tanks.
Tank is probably the toughest role to be under geared at, followed closely by a Healer. You can get away as an under geared DPS a little easier simply because even in a 5 man, there are other DPS players to help take up the slack.
Now an over geared tank can do wonders for a under geared healer, and vice versa, an overgeared healer can do wonders for an under geared tank, but even an over geared healer isn’t going to be able to make up for a tank that gets one shot.
A fresh level 80 Warrior or Paladin is going to be sporting about 18-20k unbuffed. I hate to break it to you, but there are well geared mages who can hit that. A new tank needs gear and Reputation and the fastest route to both is in Heroics. But even getting in Heroics can be difficult for a new tank.
Because you level so quickly, people tend to run very few instances. In the time it takes you to put the group together you could have almost outleveled the instance. In additon, most 'leveling' specs are not idea or tanking or healing an instance. This means that Tanks and Healers don’t get a lot of time to practice and hone their skills. So not only is the fresh 80 tank under geared, but she is also still learning the basics. This can lead to some really negative early experiences and may discourage the new tank.
At this point in the expansion there are going to be a number of well geared tanks. PuGs want over geared tanks; they always have, even in tBC, and maybe even earlier.
You can do Heroics, but it will be harder for the group. If they are in Heroics, there’s a good chance they are under geared as well. There's basically very little reason for a Raid geared toon to run a Heroic anymore. The only time I run one a Heroic on Honorshammer is if I'm helping out a guild mate gearing up an alt. I joke sometimes that I should flag Honorshammer for the LFG channel just to see the reaction of the PuG when they realize they just got a T8 geared Tank for their run.
So what can you do if you are a new tank? PuGs want geared tanks to run Heorics, but you can’t get geared unless you get the gear from Heroics. So you need to run Heroics to be able to tank Heroics. It’s something of a Catch 22.
Here's what I would do:
First, try to run with friends whenever possible. They tend to be more forgiving and gentler with their advice.
Second, make friends with a healer, someone who knows you and trusts you as a tank. On most realms, it's very, very easy to get 3 DPS for Heroics if you already have a Tank/Healer combo. Then if one of the DPS has a problem with you as a Tank, politely tell them they are free to leave the group and you'll replace them with one of the many DPS in the LFG channel.
You could also run as your offspec, DPS or Heal (if available to your class), which ever you prefer. It would be polite to tell the group in party chat you are rolling on Tank gear, as a courtesy.
Whatever you do, you need to farm gold like its your job. The best gems and enchants can go a long way to getting you to feel 'geared' to your PuG healer.
I’ve got a ‘shopping list’ below that can help bridge the gap a little bit.
Run double stamina trinkets. Raid geared tanks run around with 30k unbuffed HP. Most DPS is approaching or over 18k. Right or wrong, PuGs tend to judge you by your HP pool. Double stamina trinkets are a great way to get into a group. Once you are in, you can swap your trinket to an avoidance, or defense trinket.
Run a Normal. You are likely going to need to farm Seal of the Pantheon which drops in Normal Halls of Lightning. By running Normal dungeons, you can get valuable practice in your Tanking skills as well as to start learning the pulls and gimmicks of the bosses. As a level 80 running a Normal, you actually might overgear the place a bit, which will make your PuG partners very happy. This is also a terrific way to make some friends, and maybe even find that ‘pocket healer’ we all know and love.
Try to get your guild to take you on their Naxx10 runs if they still do that. If they don't try to organize an Alt Naxx10 to get some gear. Most Raid geared toons have been playing for a while, they may have multiple level 80s.
Finally, try targeting the 'easier' Heroics like Nexus, Utgarde Keep, etc. My first Heroic was Utgarde Pinacle. Not the ideal place to try to start out.
Do everything you can to improve you gear outside of dungeons and drops. Here is a quick list of gear you can buy with enough gold. Everything you see here is a Reputation Reward, a BoE drop, or a BoE Crafted item.
Helm - Tempered Titansteel
Neck - Burning Skull Pendant or Titanium Earthguard Chain
Back - Cloak of Peaceful Resolutions
Shoulders - Crusaders Square Pauldrons
Chest - Icebane (lots of stamina and you'll need it for Sapphiron/Hodir as some point)
Bracers - Bracers of Dalaran's Parapets
Hands – Daunting Handguards
Belt – Waistguard of the Risen Knight. If you really want to spend some cash Indestructible Plate Gidle
Legs – Daunting Legplates
Feet - Tempered Titansteel. Again, some major league cash will get you Spiked Deathdealers
Ring - Signet of the Accord
Ring - Titanium Earthguad
Shield – Titansteel Shieldwall
Addendum: As far as weapons go, I hope you did Ragemane's Flipper, a quest in Zul'Drak. It rewards the best tanking weapons you can reliably get. After that, you really need a drop. You can also try to get by with a Fang of Truth, or a Titansteel Bonecrusher. Those aren't ideal, but should be options if you vendored the quest rewards from Ragemane's. They should hold you over until you see a drop. You can also start the Argent Tournament as early as 77. There is the Axe of the Sen'jin Protector which you can purchase with Champion's Seals. From the Comments: Blade of the Empty Void, it's a quest reward from an Icecrown quest (Tirion's Gambit), and it provides +19 def.
Hopefully some of this advice will help you fight the uphill battle of a fresh level 80 tank.
If you happen to be grouping with one of these guys, let me encourage you to cut them a little slack. They are trying to gear up just like you.