A tumbler is used to hide/disguise/make it difficult to prove where bitcoins came from.
It might help to first understand that every bitcoin transaction, right back to the genesis (very first) block is available for public inspection in the block chain.
Note that the actual bitcoins are not trackable, only the amounts, addresses and the transactions - this is important.
To be able to complete a transfer of bitcoins, you need to know the private key for an address AND know the transaction ID of an unspent transaction sending bitcoins to that address - You don't just send someone 1BTC, you send them 1BTC out of the 1.2BTC you received from person X. In other words, the balance of an address is the sum of the unspent transactions and each transaction clearly shows where the bitcoins came from.
A tumbler attempts to sever the links between your old address and a new address by sending coins from you to other people and coins from them to you. It also randomizes transaction amounts and sometimes adds time delays to the transactions.
Generally there should be no link between the original transactions and the final address of the coins.
How does a bitcoin tumbler "launder" bitcoins?
This is probably answered above
Is a tumbling a viable laundering scheme?
Yes, provided that you are tumbling a small amount of BTC compared to the total volume going through the tumbler (I have no idea what the ideal ratio is). Remember also that the tumbler will give out other peoples coins. If all the coins going through a tumbler are stolen, you're going to receive stolen coins back, they just won't be linked to the coins to started with.
How would tumbling be made a more/less successful?
See answer to 2.
Edit: Take a look at https://blockchain.info/taint/1AYdAw8CcrQ2wx55LTbFHRn5bxgNZhaRLW - this shows that 6.6% of the coins at that address came from 1nWxbsMV7XKp7zi2Pq8FzK9HfoPTnBwKV - you can trace it all the way back to when the coins were mined