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I am using an Arduino SMD UNO r3 board ,and connecting thermal sensor MLX 90614 , wifi modem ESP 8266 , a buzzer and an arduino based sound sensor . How much power distribution will it require ? What should be the capacity of the battery ?

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You need to create a power budget. This means pouring through the datasheets of each component and finding the max and nominal current consumption info and then summing it up. From this, you should be able to come up with a battery capacity value.

There is a great article called "What is a Power Budget" written by Chris Gammell (from The Amp Hour) that goes into power budgets in more detail. Here are the key items from that page:

So what is a power budget? Much like a budget you might have for your personal finances, a power budget shows where all the possible power will be used by a device to by breaking it down into components and categories.

As you can see, not much more is required than your datasheets and a spreadsheet type program. ... The first two columns (A&B) are simply identifiers to allow you to recognize which components correspond to which set of data. The next two columns (C&D) determine the multiplicative factor. If you have 5 components that contain 4 op amps per, then that will consume 20x the power of a device that has the same supply current needs but only one op amp per and there is only one on the board. The next two columns (E&F) show how much current each individual component contributes and then the sum of all the components of that type contribute. Note that this parameter on a data sheet would be listed as “supply current” or “active current”. The “quiescient” number is when the device is in a resting state and will likely be much less than the active number (and not relevant for this example). Finally, the supply voltage is listed (in column G) to calculate power (using the formula P=I*V) which is listed in column I per device. All of these contributors are summed, an efficiency is estimated (I assumed a poor efficiency linear type supply) and the total power required input to the device is given. Further calculations could result from much of this initial data.

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