You (or the primary account holder) would need to do this from your account management on My Verizon.
To find out how see www.vzw.com --> Support --> Account. In Search type "Block a Number". To actually implement it, you have to be the primary account holder and log in to "My Verizon".
By the way, you could more easily have found this by searching this forum instead of posting and waiting for an answer.
I'm trying to figure out of we can block text messages from an individual on our HTC Thunderbolt. Thanks!
SIgn in to My Verizon, if you scroll down, there will be a box that says Block Calls & Text Messaging. Click it, and it will have you enter up to 5 numbers to block for 90 days. Just remember to come back in 90 days and re-enter them. It's completely free.
I'm using an app call Call Control by Kedlin Company. It's in the Android Market.
It blocks calls (I hate telemarketing calls on my cell phone) and texts.