To secure a personal Microsoft Account ("MSA", formerly known as "LiveID"), you can enable two-step verification ("MFA" for Multi Factor Authentication) easily. This article shows the How-To.
The Microsoft support article About two-step verification informs about the necessary steps.
Secure your MSA
I wanted to add MFA to an existing MSA *@outlook.com. To make it short: Open the Security basics page (https://account.microsoft.com/security).
Click update info, enter (or confirm) your mobile phone number. You get a SMS with a security code.
After you confirmed that code in the portal, you can follow the next steps.
Click "Set it up now" and choose your target platform and "Next".
Now, you get the app store link and can install the app from the store (if you haven't already installed it).
Add that, add the MSA to your mobile app: Enter the email, password, send a SMS to the device, enter that code.
When done, click "Next" (in the page above). Now there follows the "Finish" message.
Ok. Actually we are done.
To check the settings, open the link "more options". You will see your mobile phone number and some options.
You should see that the account is protected by two-step verification as here (or open https://account.live.com/proofs/Manage/additional anytime).
FYI: in my case it took a minute and I rechecked with the link "Turn on two-step-verification".
In the "Additional security options", you can set app authentication, recovery codes, remove that account and much more. So, this page is very helpful for managing MSA.
Login to any your Outlook portal (https://outlook.live.com/owa/). After entering the login and the password, the login page waits for the verification.
Your mobile app should pop up with a confirmation. The second factor needs to be confirmed outside the login process as here in the mobile app.
Hope this quick step-by-step article helps to secure your Microsoft Account(s)!