I am not familiar with batteries at all, but I just want to know how I can charge them faster? slower? with constant voltage or current?
If I want to charge a Flooded Lead Acid battery with a power supply. By looking at the graph of the charging stages of lead acid batteries, in the first stage it requires constant current with increasing in voltage and in the second stage current will decrease and voltage will decrease a little bit. Finally, current still decreasing and the voltage decreased a little bit. Now, can I just set the power supply voltage to 14.4 V since it is six cells and limiting the current to the maximum rate of charge current. Then If I see the voltage dropped based on a value in the datasheet, I can say the battery is fully charged? if this is the correct way to charge the flooded lead acid battery, if I want to charge it faster, I can only increase the current during the first stage only with keeping the power supply set to 14.4V?

 

Yes, you can do that.
The maximum charge current should be about 1/10th of the batteries ampere-hour rating.

....Then If I see the voltage dropped based on a value in the datasheet, I can say the battery is fully charged?

You can leave it at 14.4V until the current (not voltage) has dropped to about 5-10% of the maximum charge rate.
Then it should be fully charged.

If you want to maintain the charge, you can trickle-charge it at about 13.5V.

 

By looking at the graph of the charging stages of lead acid batteries, in the first stage it requires constant current with increasing in voltage and in the second stage current will decrease and voltage will decrease a little bit.?

It doesn't "require" any specific charging regime ( as long as current is not too high ...C/10 is recommended) ... think of a car battery , charging level is related to revs of the engine which vary all the time ..

Flooded lead acid is the most forgiving of any battery type , if you overcharge it electrolysis of the water/acid occurs , which is no problem , just means you have to top up regularly,

 

I am not familiar with batteries at all, but I just want to know how I can charge them faster? slower? with constant voltage or current?
If I want to charge a Flooded Lead Acid battery with a power supply. By looking at the graph of the charging stages of lead acid batteries, in the first stage it requires constant current with increasing in voltage and in the second stage current will decrease and voltage will decrease a little bit. Finally, current still decreasing and the voltage decreased a little bit. Now, can I just set the power supply voltage to 14.4 V since it is six cells and limiting the current to the maximum rate of charge current. Then If I see the voltage dropped based on a value in the datasheet, I can say the battery is fully charged? if this is the correct way to charge the flooded lead acid battery, if I want to charge it faster, I can only increase the current during the first stage only with keeping the power supply set to 14.4V?

Go to Battery University.
In general for flooded batteries 50% of capacity until 85% is reached, then 10% until 95% and then 1% unitl 100%.
Remember that a 400 CCA battery has 200 amps available for consumption, any more and the battery is destroyed. So you can charge fully discharged 400 CCA battery at 100 amps until it reaches 85% then at 20 amps then 1 amp top off.

 

As mentioned above, Battery University has some good info:

https://batteryuniversity.com/learn/article/charging_the_lead_acid_battery

 

It is very important to realize that if you overcharge the battery sufficiently you will get hydrogen and oxygen liberated from electrolysis of the water in the electrolyte. This mixture is explosive (reassembles itself into water, with considerable enthusiasm), so a well-ventilated space is required, as is care not to introduce any source of ignition - such as a spark from disconnecting the charger. Usually the hydrogen, which is much lighter than air, dissipates easily, but if you were to charge in a closed battery box, you could get a dangerous buildup of the gas mixture.

If you allow overcharging, the bubbling of the hydrogen and oxygen coming off the plates can carry some electrolyte out of the cell vents. The electrolyte is diluted sulfuric acid, which is corrosive to lots of things, including eyes, skin, and many metals.

 

So you can charge fully discharged 400 CCA battery at 100 amps until it reaches 85% then at 20 amps then 1 amp top off.

Normally it's recommended you not charge a lead-acid battery at no more than 1/10th of it's ampere-hour rating.
The CCA (cold-cranking-amps) rating is only for short-term starting conditions.
100A continuous charging current is way too much for a standard car battery.