Download replays
I use Starcraft 2 All-replay, which can mass download pro/semi-pro replays. Try to download them in the order that you'll watch them. Alternatively, search teamliquid for replay packs, preferably from players with a rating slightly above yours.
Watch replays offline
Much faster for older replays since you don't have to log in each time you change versions. Simply use the guest account instead of your main.
Setup:
1. Start SC, choose "Play as Guest", pick one and enter.
2. Click "replays", choose one like "multiplayer", and "Create new folder". Log out.
3. Find your folder in "My documents\Starcraft II\Guest1.1@1\Replays\Multiplayer". Download all replays into this folder.
Use a RAM Drive
Replays normally pause every few seconds in order to save state, which enables replay rewinding. The data is saved to your primary disk, which is either slow (hard drive) or vulnerable to wear (SSD). Solve both with a RAM drive:
Setup:
1. Pick a software RAM drive, such as RAMDisk
2. Download, install, and set it up with minimum 250MB of RAM, more if you can spare it.
3. Move Starcraft's temp folder. Edit "environment variables" somewhere on your PC, and change the value of "TMP" from "%USERPROFILE%\AppData\Local\Temp" to wherever your new RAM drive is.
4. Restart your computer. When you're done watching replays, change the temp folder back and turn off the RAM drive. Optionally you can leave it on, but it'll need more space for other programs.
If you have any other tips, feel free to share!