As far as I know, Dogecoin will only have 100,000,000,000 coins in total. But how can the supply of coins remain uncapped? How could it produce unlimited dogecoins? Is there any specific skill to make the block provide unlimited coins?
The amount of bitcoins is not set by a hard coded limit, but indirectly through the rules of Bitcoin's reward schedule.
Bitcoin's reward started out at 100 bitcoins per block, and halves every 210,000 blocks (approximately four years) until the block reward drops to less than a satoshi when it just stops.
On the other hand, Dogecoin's reward will only halve five times.
Then instead of halving again, it will go to a flat reward of 10k dogecoins indefinitely starting from Block 600,001. Therefore, it will continue to grow slowly without limit.
Also see my answer here: Reward schedule and maximum number of dogecoins?.
Bitcoin has a limited amount of coins too. They do that because the block reward is halved every 210000 blocks. If Dogecoin have something similar, then there is also a limited amount of Dogecoin. If you want unlimited amount of a certain cryptocoin (which is pointed out by Recall as something you don't want), you can for example not half the block reward.Then you'll get infinite amount of coins over time. However, this can NOT be done for a coin as bitcoin or dogecoin, as they already have a limited supply. It cannot be changed somehow. You have to make your own coin without limit (thanks Greg Hewgill)
See also the question here, and especially the following equation:
Dogecoin does not have a limit anymore.