The process couldn't be easier. Simply make sure both computers are turned on, connected to the same local network, and logged into the same Steam account. If all that's set, a pop-up will appear in the lower-right corner of your screen, letting you know you're connected to your primary machine.
Your Steam library will be shared between the two PCs, and a Stream option will appear for games that are installed remotely. (You'll need to install the games you want to stream on your host PC first, of course.) If any of your games are installed on both machines, you'll be able to choose whether you want to stream it or play it straight from the PC you're holding.
If you want to try to play a game that isn't offered on Steam, try adding it via the Games > Add a Non-Steam Game to my Library option on your host machine to try and force the matter. Valve's streaming FAQ says that might work, but warns that streaming non-Steam games is not officially supported.
Trouble-shooting Steam in-home streaming
Troubleshooting streaming problems is also fairly straightforward, assuming your hardware and home network are up to snuff to begin with.
If your games are doing the jitter-bug—in-home streaming handles latency by dropping the frame rate, rather than dropping the picture quality, for some bizarre reason—open Steam on your client PC and head to Steam > Settings > In-Home Streaming in the menu bar. Under the "Client options" portion, you'll see options for Fast, Balanced, and Beautiful, with Balanced enabled by default. Try dropping the setting to Fast.
If that doesn't do enough, click Advanced Client Options, then open the Limit Resolution To drop-down menu and select a less pixel-packed streaming resolution option. With my setup—a hardwired Core i5 desktop PC streaming to various laptops over 802.11n—dropping the resolution to 720p helps even action-packed games stream with few hitches. (The frame rate can still get a little hairy in particularly explosive and fast-paced scenes, though.) My Wi-Fi doesn't have to struggle for airspace with competing networks in my rural abode, however.
What, that didn't fix the problem either? First, make sure the Enable hardware encoding and Enable hardware decoding options are, in fact, enabled on your host and client machine, respectively—they should be by default. You can also try enabling the Prioritize network traffic option on your host machine, or switching your router to the less-trafficked 5GHz spectrum band (if your router supports the 5GHz band). If that doesn't work, it's time to break out the Ethernet cables. There's a reason Valve recommends using wired connections—they're stronger than wireless ones.
That should be about it. While Steam's in-home streaming has officially dumped its beta tag, don't be surprised if you run into occasional frame rate or input woes, as the technology is still in its early days. Some games might not play audio, or they might refuse to launch whatsoever. More frantic games may have hiccups. Again, Hayden Dingman's hands-on with Steam in-home streaming can give you a good overview of what to expect.
All that said, it's held up remarkably well for me thus far. Sure, the introduction of Steam in-home streaming is meant to pave the way for living room-ready Steam Machines and make Steam for Linux's paltry (but growing) library less painful, but it's great being able to game on your laptop while you're lounging on the couch or lying in bed. Merely plugging an HDMI cord into your laptop can bring your entire Steam library to your TV, and in-home streaming also brings the full Windows-based Steam catalog to Linux and Mac computers without the need for complex technical tricks.
Yes, Steam's in-home streaming truly feels like magic, even though it's not quite perfect yet. And once you've played a beastly modern game on a crusty old laptop that normally starts dropping frames when the word "Battlefield" is merely uttered, I'm sure you'll agree.