One can perform penance to Lord Indra by doing a Samvatsara Vrata. The presiding deity of this vrata is Indra.
There is interesting story described in Adi Parva-Sambhava Parva - Chapter 122- Of Mahabharata , where there is story of birth of Yudhisthira ,Bhima and Arjuna. Pandu father of all the pandavas performed the penance to Indra by keeping this vrata for one year.
This story is associated with birth of Arjuna ,Pandu performed Samvatsara Vrata of indra as he wanted a very superior son who shall achieve worldwide fame. Rishis adviced Pandu to perform penance to Indra to obtain a boon for a very powerful son who will defeat humans , daityas and danavas etc. in battle.
तत: पाण्डुर्महाराजो मन्त्रयित्वा महर्षिभि : |
कौरव्यो व्रतं सांवत्सरं शुभम् ||25 ||
उग्रं स तप आस्थाय परमेण समाधिना
आरिराधयिषुर्देवं त्रिदशानां तमीश्वरम |
धर्मात्मा पर्यतप्यत भारत ||27 ||
तं तु कालेन महता वासव:
P.257 - After this, the Kuru king Pandu, taking counsel with the great
Rishis commanded Kunti to observe an auspicious vow for one full year,
while he himself commenced, O Bharata, to stand upon one leg from
morning to evening, and practise other severe austerities with mind
rapt in meditation, for gratifying the lord of the celestials.
The brief procedure of penance by doing Samvatsara vrata of Indra is also describe in the chapter. Its said that pandu performed penance of Indra by Mind , speech and deeds. He meditated upon Indra in fullest of his concentration and standing on one leg from sunrise to sunset for one year. And then Indra then granted him the boon of powerful son as he desired by satisfying with his penance .
So basically the penance of Indra can be performed by one of the method called Samvatsara Vrata . And as describe in Mahabhhrrata one can get boons from Indra by performing tapas by this way . This penance has to be performed for full one year in which one has to meditate on Indra with full devotion and concentration along with control of mind , speech and deeds.
We here can read this story of Pandu's penance of Indra in Hindi.