"Inform" used to mean "to tell, to give information to, to notify." Increasingly, I am seeing it used to mean (I think) "to affect, to determine," as in this opening sentence from a recent blog entry:
"Although my blog entries rarely focus on my religious beliefs and practice, I like to think that those beliefs and practice inform many of my entries, as they inform most of my life."
Am I right in thinking that this is a new meaning of the word "inform"? When and how did this new meaning get started?

Whether or not this is a new meaning depends on how you define "new". The relevant definition is listed first in the online OED:
1. a. trans. To put into (material) form or shape; to form, shape, frame, mould, fashion. Obs.
1590 SPENSER F.Q. III. vi. 8 Infinite shapes of creatures..Informed in the mud on which the Sunne hath shynd. 1621 BURTON Anat. Mel. II. iii. v. (1651) 345 If he found her, he may as happily find another; if he made her..he may as cheap inform another. 1643 SIR T. BROWNE Relig. Med. I. §35 And so Omniety informed Nullity into an Essence.

So if 400 years and counting qualifies as "new", then yes, this is a new meaning of the word.

Isn't there a saying about being so old it's new again.

I'd say that the usage BaselAnnie has noticed is M-W's 2:

to give character or essence to <the principles which inform modern teaching> b: to be the characteristic quality of : animate <the compassion that informs her work>

This is not obsolete.