How many batteries can be connected to an inverter?

Firstly, it depends on the design of your inverter. 

One inverter may have DC terminals which can only connect one battery to, while the other models have two or three sets of DC input terminals which can accept more batteries at the same time. For example, Carspa P series inverter, 1000W, 1500W and 2000W only designed with one set DC terminals, 3000W and 4000W can support two batteries to be connected at the same time. It is easy to understand.

Secondly, total power consumption. 
Calculate the total power requirement by adding the watt usage of each appliances. It should include all the home appliances and devices you want to connect to the system. While calculating the wattage, remember that large appliances such as refrigerators and microwave would need surge power to start them up and there is power consumption of inverter while working. So please consider the extra energy to compensate for the additional energy demand.

Thirdly, inverter input voltage.
Most of the inverters would have 12V or 24V input. Some inverters may have 36V, 48V, and 96V as well. So first, you need to check what input voltage your inverter featuredCheck whether your battery matches the input. If yes, just connect the batteries properly. While your battery doesn’t have to be a specific match. Ensure that the total batteries in series or in parallel match the inverter voltage will work.
If your inverter is a 24V unit, connect your batteries in series (+ terminal to - terminal of the next battery) the voltage adds up. So you can get 24 V with 4x6 volt batteries, or 2x12 volt batteries.If the battery voltage matches and you want to increase battery capacity, connect the batteries in parallel (all + terminals connect together and all - terminals connected) then the amp-hour capacity adds up with voltage staying the same. In a battery bank all of the batteries should be with the same voltage and capacity.

 Fouth, hours to run the inverter
The duration is crucial. Energy supply is calculated based on the number of hours the battery runs. Find out how many hours you are going to run your appliances.The rated power multiples the running hours and you will get the total consumption of each device. The total watt will be calculated based on the number of hours, and you can decide the battery capacity.
Let’s say you have a 4000Watt, 24V inverter. You plan to run a 700W toaster and 1000W coffee maker for approx 2 hours.
Total consumption=(700W+1000W)X2Hrs=3400W.h
The needed battery capacity: 3400W.h/24V/0.8=177Ah
So, a 24V 200Ah battery bank can last for 2 hours to power these two appliances.

Fifth, battery storage capacity.
The battery capacity shows how many hours the system will run and supply the energy.The battery capacity is measured in amp-hours. Based on the above calculation, the system would require 200Ah of batteries. It can be 4X6V 50A batteries or 2x12V100Ah batteries. The quantity depends on the battery capacity.