Stadia is an incredible proof of concept under ideal circumstances, but the delta between the best and worst game streaming experience can be huge: a crappy connection can introduce input lag hamper visual fidelity. If your gameplay is feeling sluggish, there are a number of things you can try to improve your situation — and depending on how tech-savvy you are, they may not all be obvious.
Make sure your connection can handle it
This one is kind of duh: be sure your internet connection passes muster. Google's requirements are actually pretty low — download speeds as slow as 10 megabits per second are technically viable, although you'll only be able to play in 720p. For the highest-quality experience, you need speeds consistently over 35 megabits per second. That's just for Stadia, though; if your household is liable to be using your bandwidth for other activities while you're trying to play, you'll need to factor those uses in. You can check Google's official Stadia speed test page here.
Be mindful of other bandwidth-hogging activities
Streaming Netflix in 4K requires almost as much bandwidth as Stadia: 25 megabits per second. Combine the two, and you're looking at 60. Ditto YouTube, Spotify, and whatever other odd downloading may be going on in your home. If you've got roommates or kids, you'll likely either need a particularly robust connection — in excess of Google's official requirements — or to carve out times when enough bandwidth is available to maintain your desired level of stream quality.
Use Ethernet if you can
Bypassing Wi-Fi altogether is your best bet at wringing the fastest connection possible out of your ISP. The wall adapter included with Chromecast Ultras actually has an Ethernet port built in; you should use it if at all possible. Same goes if you're playing on your PC. (You can even hardwire your phone if you really want to, but this all starts to feel impractical at that point.)
If Ethernet isn't an option, try 5 GHz Wi-Fi
If you can't (or don't want to) run Ethernet to your gaming device, 5 GHz Wi-Fi is the next best thing.
The majority of Wi-Fi connections (as well as other types of wireless connections) operate at a frequency of 2.4 gigahertz (GHz). That's generally a good thing; 2.4 GHz signals have a long range and can pass easily through walls and other obstacles. But because the frequency is so popular, there are 2.4 GHz waves all over the place, and all that traffic can cause interference that puts a damper on streaming performance.
Most modern Wi-Fi routers are also capable of transmitting in 5 GHz, which, in addition to allowing for higher speeds, is less prone to interference by virtue of being less widely-used. The drawback is that the frequency is less able to penetrate solid objects, so if your router is two rooms away from your TV, it might not help performance. Enabling 5 GHz is a different process for different routers, so you may need to do some research to figure out how to set it up for yourself.
Prioritize traffic to your Stadia device
A lot of newer routers will also let you choose which device on your network gets priority in the event of competition for bandwidth. Google and Nest Wifi even have a "gaming preferred" mode that'll automatically prioritize any device on your network running Stadia. It's on by default for Nest Wifi, but the older Google Wifi will need to be reset then configured again in the Google Home app to take advantage.
Like switching to 5 GHz, different routers have different software, and you'll need to do some searching to figure this one out for yourself.
Use your TV's 'game mode'
You probably know this one already, but just in case: dig through your TV's settings for something like "game mode" and enable it on the input you're using for Stadia. Post-processing (for that gross artificial motion smoothing, for example) taking place inside TVs can contribute to input lag. Game mode disables effects like that, eliminating precious milliseconds between the moment you press a button and when you see the result on screen.
When playing Stadia through a Chromecast Ultra, the device actually tries to enable game mode automatically. Whether that works depends on your particular TV model, though, so it's probably best to seek the setting out and toggle it manually.