You want to use content from a news article or television station's web site in your blog post - this could cover many things. For lawyers, news coverage about big victories in the courtroom usually means a desire to place that coverage on their bio page at the law firm's web site. The 21st Century's version of an Ego Wall.
However, as I've discussed here before on more than one occasion, if a lawyer pulls that story or that video and puts it on the firm's website willy-nilly, then copyright infringement may occur. Those media stories (including photos and videos and audio interviews) are all the copyrighted work of these media outlets and should be respected.
What to do? First things first, just ask. Call or email the media source (this is really easy if you have the contact information of the reporter who just did your interview) and ask permission. Alternatively, surf their site for words like "reprint" or "permission" and you will find things like this:
San Antonio Express News
Dallas Morning News
Houston Chronicle
The Associated Press.
Will you have to pay? Maybe. It's called a "licensing fee." Balance that cost against dealing with a cease and desist letter (if you get one, Righthaven never bothered) or a claim for copyright infringement by the media's IP litigators.