I have been away from the Glade for a while, but I know where to go when I need advice. Just recently a tournament player moved tour area and started gaming with our LGC. He plays Dwarves and Skaven, and I recently played against him with a theory hammer list (3 Alter characters). The list I brought was created for a newer player, so I took a list that was not over powering, but I ended up playing the new guy. I was slaughtered. I haven’t sustained a beating like that in quite a while. Now I am not mad or bitter at the list he brought and the person himself was very nice and enjoyable to play against, but he self admits that he thinks about the list he brings and he exploits what the individual army books give him. I don’t have an issue with that and I approach this as an opportunity to improve myself as a gamer, but I think I need some assistance because I had a hard time figuring out in the game how to deal with some of his units.

This is what he basically had:
• Anvil of Doom
• Longbeards
• Thunderers
• Slayers
• Grudgethrower
• Bolt throwers
• Organ Gun
• Gyrocopter

What is funny, but he brought a list that is similar to one that I have been contemplating. He played this list like a true gunline. He hid his units from me and used the anvil and gyrocopter to get some precious kills. When he killed enough of my units to draw me out into combat, I got splattered with the grudge thrower and organ gun.

I have all units available to me so I am not limited with what I can bring to the table, but how do you all (in specific examples) deal with a dwarven gunline, especially the organ gun, gyro, and anvil?

The anvil just plain sucks . . . so you'll just have to take whatever that puts out.

I usually try and take out organ guns ASAP. And you have to rush them. By flooding the "zone" with several fast units (say War Hawks, wild riders and glade riders) he will take out some but you should get all the way through. Cav mounted heros in units work well, for example a WR hero in a unit of Wild riders or treekin and move up, his unit may get shot up and crippled, but the hero itslef can charge out and take out the artilery, leave the unti to position towards something else.

Gyro copters can be annoying, but will go down fairly quickly with some sustained glade guard fire at short range.

The Anvil is one of GW's worst creations, bent beyond belief.
Usually the Engineer crewing it has the "Killing-Blow-Doesn't-Work-Ha-Ha" armour.
We do have a few advantages against Stunties.
We've got speed (Both on foot and in terms of Initiative), we've got Forest Spirits, we've got good shooting, we've got Waywatchers.
What we don't have, is any armour worth talking about, so going toe to toe with Longbeards usually ends in tears, epsecially if there's a fat chap leading them, being carried about on a shield. Avoid him, especially with any unit with a Character or Champion and don't let anything with T5 or over get anywhere near the little short-life!
How much terrain do you play with? A lot of terrain is good, enabling you to sneak up, before popping out and running like stink to get into combat, so his shooting is nullified.
One thing to beware of, is the Runed Bolthrower, S7, Flaming & Magical means that Treemen become Roman Candles very quickly!.
Slayers are fairly easy meat, they shouldn't get a Charge off and will always be hitting last due to their low I value, take them down with any infantry types troops, with a little luck, it'll take the turn you charge & his turn to bump them off, leaving you ready to charge again and get amongst the shooty stuff.
Using MSU Dryads helps getting you where you can hit his warmachines, as has been said, flooding an area with potential targets helps get something through to kill the warmachine crew.
Alter Kindred are all well & good, but there's always the risk that you'll fluff your attacks against a warmachine crew and get taken out yourself.