Translation:He used to speak to his grandmother every morning.
The translation for 'at pleje' as 'usually' is .. not a very fortunate one. 'Pleje' is a verb, of course, and should be treated as such, but the English language doesn't have a present form of 'used to'. You -could- translate the sentence like so, but I would recommend keeping the structure rather close to the given sentence.
The actual translation of 'usually', the adverb, is 'sædvanligvis', so you'd go with "Sædvanligvis talte han med sin bedstemor hver morgen."
From what my Danish friend has told me, I'm not sure "tale" is appropriate in this context. Apparently "tale" has a rather formal tone to it, and speaking to one's grandmother hardly seems like a formal conversation to me. Once I wrote to my Danish friend in an email about him coming over "at tale med mig" and he told me later that that sounded really weird to him because "tale" isn't used for a casual conversation between friends. I think "snakke" would be the word a Dane would use in this situation.