"Palatalization" means that a consonants is pronounced with the middle part of your tongue raised towards the roof of your mouth. This motion similar to what you do when pronouncing the "y" in "yes", only simultaneously with pronouncing the target consonant.
The exact realisation is better learnt by learning from audio samples in the language you are trying to learn. I think platalalized т and д in Russian are a bit different from those used in Ukrainian because we tend to mix in a little touch of an "s"-like sound into these. Ukrainians don't (at least, not in the standard language).
Seth, today is our lucky day. http://russianmentor.net/gram/mailbag/topics/phon1.htm
It appears saying I have a typo in my answer, this is after i butchered the spelling about 5 times and have had to redo the same four questions over and over again in my practice, which was frustrating. http://imgur.com/a/8flub EDIT: Might be a missing "ь" that isn't showing up in the correction, or the "e" looks a bit different.