Blitz chess is, of course, chess with very little time. You only have the time to recognize the ideas and patterns you know very well. These are the ones you've seen many times in your own games or many times in analysis.
Some players don't have this, or can't make use of it in fast time controls. They mostly focus on not losing material to 1 and 2 move tactics.
Some players bring immense knoweldge with them to blitz games, everything from amazing tactics to fantastic strategy to exemplary endgame technique. Two GMs can produce a game of higher quality in 10 minutes than most players can over many hours.
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To answer your question, yes, I nearly always have a some kind of strategic narrative in my head, and my candidate moves try to fit in that framework. Then I calculate to check for tactics. Lazy moves are always bad, but when time gets low, of course the moves become even more intuitive, and aggressive moves will make the opponent think a little longer.
How should you follow that? Learn more about chess and play a lot of slow games. Analyze all the slow games you play. Usually the first time you miss a winning idea (for you or your opponent) you won't be able to immediately make use of it. After a few tries or seeing it a few more times in analysis of other games the ideas will start to automatically come to mind when they're available.
Do you guys always try to find a logical move? A good move? A plan based on good strategy on such short time periods? Or are there situations where you just make some lazy, aggressive or intuitive moves? If so, should i follow that?