If you got your Indonesia visa on arrival, then as per the current immigration regulations, you are allowed to renew it once for an additional duration of 30 days. But, to apply for this type of visa, it is better to inform the immigration officers of your intentions to renew at the time of getting your visa on arrival. The initial visa costs USD 25 and is valid for one month. The extended visa also costs an additional USD 25 and ensures you get one more month to stay in Indonesia.
One can get this extension done at Jakarta, Yogyakarta, Surabaya, Bali or any other city that has an immigration office that handles visa extensions. I did mine at Yogyakarta. I went on a Friday afternoon to just understand the process, but thankfully, I had all the necessary documentation to file my visa extension on the same day.
The front desk at the immigration office hands you a file folder with the visa extension form. After that, I took a token to understand the process at the immigration counter. Here I was told that I need to provide the following:
1) Passport with Indonesia visa in it and Indonesia departure card
2) Duly signed and completed visa extension form
3) 1 copy of passport
4) 1 copy of Indonesia visa
5) 1 copy of Indonesia departure card
I was told to leave the documentation behind and come back on Tuesday morning to pay the fee of 250,000 rupiah or ~USD 25. I paid the fee on Tuesday morning and came back to collect my passport with the extended visa (a new stamp next to the visa sticker) on Tuesday afternoon. In sum, I got my visa extension done in 3 days without any sweat. The imigrasi office at Yogyakarta (Jogja) is very professional and prompt. They live up to their timelines. I have heard pretty bad visa extension stories in Bali and Jakarta and I am happy that I did mine at Yogyakarta. If you plan for a visa extension in Indonesia, I would recommend getting it done at Yogyakarta.