It's not easy using Google services when your Internet connection is very slow. Here are some helpful features:
1. Gmail's basic HTML mode - https://mail.google.com/mail/h/. It doesn't have all the features of the regular Gmail interface, but it lets you read messages and compose mail. The basic HTML interface is better suited for slow connections. You can even set it as the default interface.
2. YouTube Feather is an experimental interface that's intended to "serve YouTube video watch pages with the lowest latency possible". You can still play videos, check related videos, subscribe to channels and read a few comments, but these are all the features that are available. Since your connection is slow, it's a good idea to select "240p" from the list of resolutions.
4. The old Google image search interface is better for slow connections, but you should bookmark this URL to use it. Unfortunately, you can't switch to the old interface and the "switch to basic version" is placed at the bottom of the page in the standard version.
5. Google Public DNS is a simple way to speed up your browsing experience if the DNS service you're using is slow. "The DNS protocol is an important part of the web's infrastructure, serving as the Internet's phone book: every time you visit a website, your computer performs a DNS lookup. Complex pages often require multiple DNS lookups before they start loading, so your computer may be performing hundreds of lookups a day," explains Google.