How do American soldiers get to war zones?

I know alot of US Military personnel pass through, for example, Shannon Airport (a contentious issue locally) but are there still sea going troop transports?

They’ve been using chartered commercial aircraft for a long time now.

They use anything which works. Ships, trucks, planes, including chartered flights, private air, and military transports.

Most are via chartered air. ATA, I believe. Of course, if there’s big equipment to be moved, it’s different. We don’t fly into the country though. We land in another country and drive in or fly in on our military stuff. C130s and the like.

http://en.wikipedia.org/wiki/Military_Sealift_Command The Military Sealift Command operates a wide array of support ships. (Classified as civilian-auxiliary.)

The military still operates amphibious assault ships for rapid reaction forces. (LHD’s and LHA’s.)

If it is routine troop transfer and rotation, the military charters jets. Heavy equipment may be moved by sea.

For some items, the troops rotating in to Iraq can use the equipment left behind by the troops rotating home.

We stop in Shannon to refuel. It’s usually not longer than an hour or so. What’s the issue the locals are having?

The Republic Of Ireland is a neutral country so shouldn’t be lending logistical support to warmongers is the jist of it from the Anti-War groups.
http://struggle.ws/wsm/shannon.html

Also, some are concerned that allowing American planes to refuel there makes it a target for Islamist terrorists.