Official: how Google handles redirects

What is a redirect?
A redirect is between two pages. For example, you enter the URL of page A in your web browser. Page A tells the browser that the actual content can be found on page B. The browser goes to page B.
There are different redirect types that you can use to tell web browsers and search engine robots that the content can be found on a new page.

301 permanent redirect

If you use a server-side redirect, the web server returns the redirect as soon as you try to access the page. The user never sees any of the content of the initial page.
A "301 permanent redirect" is a server redirect that tells search engine robots that the old URL should not be used anymore. The new URL should be used instead.
This is useful when you change your website URLs for good, for example when you redesign your website.
302 temporary redirect
A 302 redirect is also a server-side redirect. The difference is that a "302 temporary redirect" tells search engines that the URL might change. According to John Mueller "search engines tend to index the content (and keep all signals) under [the original URL], since it’s unsure that it’ll always redirect to [the new URL].
These temporary redirects are useful for redirects that depend on the user's country, device, or language settings.
JavaScript redirects
A JavaScript redirect is a so-called client-side redirect. That means that the web server first shows the original page. The initial page tells the browser that the content is on another page.
According to John Mueller, "caching depends on the server settings, and search engines have to guess at what you’re trying to do (index under [the original URL] or [the redirected URL]?)."
Meta refresh-type redirects
These redirects are similar to JavaScript redirects. A meta tag on the original page redirects the browser to a new page. These redirects are not recommended.

303 redirects, 304 redirects, and other things
It's usually not recommendable to use these redirects. Here's what John Mueller says about them: "If you have strong feelings about one of the other kinds of redirects, feel free to use them. We’ll have to figure out which URL to index the content under, so if you have strong feelings about that too, make sure to follow up with other canonicalization signals."
You can redirect as many URLs on your site as you want at the same time. However, you should keep the redirect chain as short as possible. Google follows up to five redirects in a chain.