Kartika Vrata is a special time to worship Radha Damodara, and especially get the mercy of Radhika, since it is Her month, and She is very very easily pleased this month if one worships Her along with Her beloved Damodara.
Srila Prabhupada on When to Start Kartika Vrata: "In Vrndavana we should have Kartika Vrata, Urja Vrata, for one month beginning on Ekadasi (Pasanukusa)
Pasanukusa Ekadasi Morning: Offer prayer-"O Janardana, O Damodara, O Devesa who are accompanied by Radhika. During the month of Kartika, I will bathe early every morning for Your satisfaction."
1. Rise early every day by Brahma Muhurta, bath, chant japa offer Mangala Arotik
2. Hear Srimad Bhagavatam, especially Radha and Krishna pastimes in Vrndavana, daily in association of exalted Vaisnavas, if possible. By regularly reading Srimad Bhagavatam during Kartika month, one gets the benefit of reading all the eighteen 18 Puranas. All other duties should be given up in favor of hearing the scriptures from sadhus during this month.
3. Chant continually in japa and kirtan, Krishna nama, do extra rounds and more kirtana with family.
Give up favorite food article for entire month (sweets, salties) Try to eat only once in a day.
Eat your meals only on palasa leaves (if possible, will give tremendous punya.)
No oil on body and NO EATING honey, eggplant, portal, pickles, red rajma beans, or sesame seeds, or urad dahl (no kichoris)
Daily sing the Damodarastakam, meditating on meaning
Daily offer a ghee lamp to Krsna Deity or photo (no need of picture of Mother Yasoda-Damodara or photo)
Daily offer arotik and prayers to Tulsi devi praying for eternal residence in Vrndavana and eternal service of the lotus feet of Radha and Krsna.
Daily chant the Radha-krpa katakasam, and Krsna krpa kataksam in Giti Guccha songbook
Also chant other prayers to Radha and Radha Krsna Yugala from the Giti Guccha songbook
ON Ekadasi, Dvadasis, and Purnima chant the one-thousand names of Radha
On the three Ekadasis in Kartik try to observe Nirjala Vrata and stay awake chanting hari nam, especially on the last one, Uttana Ekadasi, when Lord Visnu and all the demigods awake after four months slumber.
Donate charity to pure devotees
Offer special nice foods to Krsna for entire month. For example every day make sweet rice,(khira) which is the favorite food of Krsna.
BAHULASTAMI BATH IN Radha KUNDA- "Anyone who bathes in Radha-kunda on Bahulastami becomes a dear devotee of Lord Krsna, because this act highly pleases Him." (Hari-bhakti-vilasa)
BREAKING THE Kartika Vrata FAST: After sunrise and within the paran breaking period on the Dvadasi day after Uttana Ekadasi (if you started your Kartik Vrata on Pasanukusa Ekadasi),-offer arotik to Krsna and dedicate your vrata to Radha and Krsna for Their pleasure, worship the Vaisnava brahmanas by offering them presents plus a prasadam feast including the items that you fasted from during Kartika (sweets, milk products etc.)
After honoring the brahmanas then break your Kartika Vrata fast by honoring the foods you abstained from (such as urad dahl, sweets, or whatever items.) Chant Hare Krsna Hare Krsna Krsna Krsna Hare Hare Hare Rama Hare Rama Rama Rama Hare Hare and Radhe Radhe Govinda, Govinda Radhe.....and taste the sweet feeling of spending the entire month absorbed in pleasing Radha and Krsna.
Jai Srila Prabhupada!