This blocks a number from both calling you and sending texts, you will not see or notice anything. The person texting/calling you will not be told “you’re blocked”, they just don’t get through. This done on a One M8
Alt A, number is NOT added as a contact
Inside the People app you tap the 3 dots menu in the upper right hand corner. Select Manage Contacts where you have Blocked contacts.
There you tap the + sign and either select Choose from contacts or Add number. Just select the option that fits you. Select or type number, if the number you type matches with a contact in People it brings in the contact. It will then warn that you will not get calls etc from that number since it will be blocked, just press “Ok” to accept.
To remove a blocked contact you either long-press the blocked number/contact and select Unblock contacts. Or Select 3 dots menu > Remove block contacts where you just select the ones you want to remove from blocked list and press Remove, now you get prompted if you want to cancel or OK. That’s it
Alt B, number is added as a contact (the easy way).
Inside the people app: find the person that you want to block. FInd Block contact. Tap it. Tap ok. It’s done.
Alt C, Dialer way
With Dialer active, just tap 3 dots menu and select Blocked contacts. Follow Alt A for how.