@Carlfredrik some of the themes have this as a functionality in the header section. If not available, you can check out other 3rd party apps that are available in this link : https://apps.shopify.com/search?q=instant+search Hope it helps.
@Carlfredrik that's great. Since it has a free plan, the best way would be to install and try it to see if it fits your needs. Else just uninstall and try other similar apps and find the best suited one. That's the way I usually follow. All the best.