1. The wallet generates an address.
Correct.
2. The person who wishes to send you money send the transaction to your address, then saves that to the global blockchain
No quite right - they create a tx that assigns the ownership of "unspent output scripts" (i.e. their BTC holdings) to your address (which will require your "private key" in order to themselves be assigned should you wish to "spend" your BTC holdings at a later stage).
The tx is then "broadcast" to the P2P network (not *saved* in the blockchain). Eventually this tx (along with generally many others) will be included in a "newly mined block" which is effectively appended to the blockchain (so you could think of this part as *saving it to the blockchain* if you like).
3. The wallet holder's wallet compares the blockchain every once and a while and if the transaction is on it (and verified by 6 other systems) it accepts the transaction and modifies the wallet accordingly.
The "confirmations" is simply the length of the chain of blocks that include your tx starting with the initial one it appeared in (so if your tx was in block #218212) then it would currently have 1 confirmation and assuming the block doesn't get "orphaned" (there's a whole lot more to know about that) then when the current block # is 218218 your tx will now have 6 confirmations (nothing to do with "other systems" just "more blocks").
4. The blockchain is modified to show that the transaction was completed.
No - the blockchain is never modified at all.
HTH
Thanks, this cleared up some things for me as well.
! You've actually just answered a whole bunch of things for me as well. 
