Saving tweets has now been made easier by Twitter's bookmarks feature which the company just added to the service across all platforms where it's available for use, which includes the web as well as the Android application, though you may need to update your Android app if you aren't seeing the option to bookmark a tweet that you want to come back to later on. That said, the option to bookmark tweets should be live for everyone, though it's not immediately noticeable where the feature is located as Twitter didn't actually add a new button specifically for this purpose.
To find the bookmark option you'll need to tap or click on the share button, and when you do the pop-up window that surfaces will now have a new option available - this will be the bookmark option, labeled as add tweet to bookmarks. This will save the tweet for you so you can come back to it later, which is going to make interacting with certain tweets a whole lot easier if you aren't able to interact right away, as you won't have to go digging for a tweet that you saw earlier on. That said, bookmarking tweets won't let you save them indefinitely if the tweets ends up getting deleted, so it's important to keep that in mind.
If you do save tweets to your bookmarks finding them again so long as they're still available is pretty simple. All you have to do is tap or click on your profile icon and the bookmarks page will be listed as an available option at the bottom of the menu. As an added privacy measure Twitter has made it so that bookmarks are only visible to the person who bookmarked a tweet. So while you can see all of the people that someone follows, you can't see what that person has bookmarked. You can still remove bookmarked tweets though if you don't want things getting cluttered. This feature is already showing up as live in the Twitter android app though there haven't been any recent updates pushed out to the app itself, so it's also possible that this is a server side change which Twitter simply needed to flip the switch on.