How to carry a step-through/mixte bike
Find the centre of mass of your bike, which is usually just above the BB+downtube. 

There are two strategies for carrying the bike, assuming that the bike does not have any heavy accessories such as pannier rack+bag, which would otherwise alter the centre of mass of the bike:


flat/downstairs: one hand go over the top tube, grab the down tube so that the bike naturally leaning forward. The seat should rest on to your shoulder. Your shoulder carry most of the bike's weight. 
upstairs: reverse the bike, one hand on down tube (or chainstay for a very tight stairs) with the (back of the) seat resting on shoulder. Again, your shoulder should carry most of the weight of the bike.


Downstairs/Flat



Upstairs: as Criggie has suggested, carrying on your left (non-drive side to your body) would be cleaner (although my pants are usually black and my bike has a chain guard so I have no problem). I would like to note that if you choose this option, take care not to dirty your sleeve. Holding the seat tube is a little bit awkward, you could try to hold the crank and see if it fits your style. You can also use the other hand, holding the chainstay, to guide/stabilize the bike