You can protect your tweets (lock your account) by visiting the settings page, which can be found here: https://twitter.com/settings/account and put a tick next to 'Tweet privacy' which looks like this.
Note: ticking the box in the image above does NOT affect your Twitter privacy, you need to do this on your own Twitter account. Go to https://twitter.com/settings/account to do this (& log in)
Once you've done that then people who aren't following you cannot see your timeline without your permission. You'll have a little lock symbol next to your name and people have to send a request to follow you.
However I don't think any system is perfect and from looking at the comments on a similar post (about blocking people) I wondered if this might be giving people a false sense of security (or privacy).
There are several ways in which people can read directly, or at least work out, what's in your tweets.
1. Although Twitter makes it harder for someone to retweet a locked account (the 'Retweet' button doesn't work) this can't stop someone from copying the text manually and reposting it. If you think someone reading your timeline might do this (without your permission) then your tweets aren't perfectly private.
2. Anything that is visible on the screen of a device can be captured by my making a screenshot* - this can then be posted as an image accompanying a tweet. This also includes anything written on a private Facebook page or ANY system. If you can see it on your screen you can show it to someone else.
3. If you've ever heard someone talking on a phone you're hearing just one side of the conversation but you can usually work out what the person they're talking to might be saying, from how they respond. It's possible to search for someone's name on Twitter, or their @mentions, and see what people say to them even if you can't see what they say.
Even without a conversation I might give away what you're planning to do tonight if I talk about meeting in Ye Olde Pubbe at 7.30 and mention you and a couple of other people we're meeting. Someone else watching might reasonably assume that you might be at the pub too.
* How to make a screenshot / take a 'photo' of your screen
Simultaneously press the on/off button at the top and the home button at the bottom, the screen is then saved as an image to your cameraroll.
Press the PrtScr button which is usually somewhere to the top right of your keyboard, you may need to use the Function (Fn) key to activate it. The image is stored temporarily in your clipboard which is generally hidden, but you can view and edit the image by pasting it (Ctrl+V) into Paint / Paintbrush.
If you just want to copy the currently active window use Alt+PrtScrn (thanks to @zeno001 for pointing that one out!)
To take a copy of the entire screen use Ctrl+Command+Shift+3 (you can then paste it somewhere using Command+V) but if you want to save it as a picture file on the desktop remove the Ctrl bit, ie Command+Shift+3.
To select just a bit of the page to copy use either Ctrl+Command+Shift+4, or to save to desktop use Command+Shift+4.
- What happens if you block someone on Twitter? What happens if they block you? (by me)
- Advice to celebrities about Twitter - for anyone in the public eye really (by me)