@TP
To give you a visual view about going short this month and long next month or going long this month and short next month, check the screen shoots. The examples are done with horizontal calendar spreads and the pictures speak there own words:
Short the month which is more near expiry and long the month which is more far away from expiry:
Long the month which is more near expiry and short the month which is more far away from expiry:
Depending what strike levels you choose and what combinations you make, those pictures will look different. So as told: In this example I show only the different which shows up when doing "Horizontal Calendar Spreads" the way you mentioned.
Now to your next question about squaring off. Depending what you further plan with your long leg from the next month series, you let the short leg expire and play the long leg further in what ever way you wish to do so. If there is no further plan with your long leg, then you square off the whole trade at the end of the month.
@Sabharwal
One simple way is to roll up or down your whole calendar spread or you buy back the short leg and play an other strategy with your long leg. Here you have to be flexible in your option strategy planing/thinking. No fix rules here, only experience and tested strategies which worked for you in the past. Start with paper trades with the roll up and down strategy to get a first feeling about it.
Take care and have a good start into the new week / Dan