First, I feel your pain-had to wait over 3 months to JB last year bc of where I was in the JB/fw cycle. I just realized I didn't know as much as I thought about how to use TU & the directions are fairly sparse in the program if you're new to it.
Anyway, plug it in & go to the advanced tab and make sure you have Request SHSH from Cydia checked.
Then click "Save SHSH."
This is where I got confused as to how to get my SHSH from Cydia onto a different computer. I thought that by plugging it in & clicking the request from Cydia setting it would check automatically. But you must then also click "Save SHSH" which is a little confusing. If there are any you will see them pop up in the bottom window pane area. Make sure you also have show all SHSH checked on the left too. Think that's about it. Thought I'd mention it bc I knew my iPad had like 8-10 blobs/SHSHs saved but none showed up. So if you didn't know the history of the device *and* you didn't have every last setting checked exactly correct in TU, you'd never see the blobs that might very well be there. Good luck, hope you find some!
It won't show anything until you follow the steps I outlined above to tell it to connect to Cydia and verify that the device does/doesn't have them. If you've clicked on all the things I mentioned and it's still showing that, then unfortunately you will either need to wait for an untethered JB or use RedSnow.
I personally would not recommend a tethered JB unless you are quite experienced with troubleshooting possible install conflicts, don't plan on heavy use of Winterboard/theming and you always have your laptop nearby, or if it's not your primary phone and you can afford to let it sit around unbootable from time to time when it crashes from low memory, runs out of power, etc. YMMV.
Also, please note that SSH and shsh are two *completely different* and totally unrelated things. If you're searching for info about SHSH & typing ssh you're gonna be totally on the wrong info track. I don't use ssh myself because my computer sucks too bad to reliably support it.
I JB'd the iPhone 4.3.5, and it's tethered,
I guess it's ok as long as I dont reboot
or let the battery drain. Plus I have a laptop
if I end up going on a trip.
And yes be careful what ya do when ya not around a pc with ya phone. I had a tethered jb for 2 months it wasn't that bad . It was better than a no jailbreak