Q: how to send pdf from computer to iPad

The easiest way is to use some web storage like box.net, dropbox, 4shared, etc - upload the pdfs to your storage space with whichever free service you pick, then download them to whichever app your plan to read/edit the pdfs with on your iPad.

Note that there is no general shared file space on the iPad, so you will need to load them directly into the app you use with those files (Adobe reader, GoodReader, GoodNotes or whichever app you use for your pdf files).

If you sync with iTunes on your computer, many of those apps will also allow you to simply drag and drop the files into them when your iPad is connected to iTunes, then click on sync, and they will be transferred over.

Sharing only works if you have an App on the iPad that supports it.  What app are you trying to share the files with?  Does it support pdf's and file sharing? (note if the app you want to use does not support file sharing, it should not even show up in the list to add files to).

Apple file sharing is very limited.  If this is important to you, the third party apps are much better.  I'm a big fan of Dropbox, which has a built-in PDF viewer and talks to most other major third part apps.

What about if you then sync?  In other words, if the transfer does not take place immediately, does it happen with a sync?

If not, I would disconnect the device from iTunes, perform a reset (press and hold the power and home buttons until the apple logo appears, then release and let it restart).  Then try it again.

Drag and drop file sharing should work just fine.  I've not done it with Pages as I do not use Pages, but it has worked just fine for me for numerous other apps (GoodReader, QuickOffice, other notes/notebooks apps).

Try an iPad reset (or just power off / power on first if you prefer).