Well, here is one way you can do it.
(1) Go to the Dwolla website and connect your bank account to Dwolla.
(2) Use Dwolla to withdraw money from the bank account and put it into the Dwolla account.
(3) Sign up with CampBX.
(4) Use CampBX website to withdraw money from Dwolla and into CampBX.
(5) Use CampBX to buy bitcoins with the money.
(6) Use CampBX to transfer money to a bitcoin address. You could even use the bitcoin address provided for deposits on GLBSE. Otherwise, generate an address in your client, and you will have to then send from the client to GLBSE.
(7) Now, once you have bitcoins with GLBSE, and can place an order to buy shares of any of those assets.
When a GLBSE asset issuer pays dividends on that asset, your dividends go directly into your GLBSE balance.
I suggest CampBX instead of MtGox because I know for a fact that you can move money from Dwolla into CampBX easily. I'm not sure if that's the case with MtGox or not, having not done it recently. Moving money from MtGox into Dwolla, on the other hand, is definitely something you don't want to try right now.
The specifics of when dividends are paid, etc. depends on the asset. Some of them have info on GLBSE, others have info on the forum, some both.