Excuse my ignorance, but how do I sync the wallet client to today's date?
Basically making sure you're connected to the bitcoin network, and wait untill it's sync'ed... On a slow pc, this might take a long time... Just have patience
I had no idea the process took this long, thanks for your help. Makes sense since I sent coin less than a week ago and client is still syncing from 4 years and 33 months ago. I guess I got to run client from the background on my laptop, any idea the length of time it will take to fully complete the syncing?
Depends on a lot of factors: the bitcoin core version, your internet speed, your system load, the amount of memory, disk speed, os,...
Basically, find the bottleneck that limits your speed and upgrade if possible, otherwise you'll have to wait... If you're using linux as an os, the top command is really usefull, if you're using windows, you'll need to ask advice from a windows pro on this forum.
IIRC, last time i sync'ed on my server, it took me about 48 hours to sync... But that was on a server (2*4thread XEON, 16 Gb RAM, RAID 1 15krpm disks, fast uplink, latest core version compiled on the server, latest debian version, ...).
There are a couple of sollutions if you really can not wait untill core is sync'ed, but those sollutions are rather technical and carry some limited risk, so if you have time, i'd suggest to wait it out. In the meantime, you can doublecheck within your core version if the deposit address is 100% sure to be correct, you can backup your wallet just in case, and you can use a block explorer like blockchain.info to check if there is a confirmed transaction. If you see a transaction for your address, chances are really good that after syncing, your problem will be solved.
BTW: i see your main focus was learning/experimenting... Might i suggest to switch to the testnet for this? Testnet coins are free, so you can learn without losing real money
http://tpfaucet.appspot.com/you can also run your core on the testnet, but i'd suggest to wait untill the main net is synced before doing so, since switching to testnet will start to sync the testnet blockchain, so there will be no progress on the main net chain as long as you're running on the testnet.