Tachnun is recited until Erev Yom Kippur, together with the long Avinu Malkeinu. One must use these days to correct his ways and do Teshuvah. A doubtful Aveirah requires more Teshuvah than a definite one, as it is human nature to discount a doubtful Aveirah and assume that he didn’t really do anything wrong.
One should increase in Torah, Tefillah and Tzedakah. One should be more meticulous in his observance of Mitzvot, even where he is ordinarily accustomed to following the lenient opinion. The seven days between Rosh Hashanah and Yom Kippur encompass the seven days of the week. One should utilize each day to do Teshuvah for all the corresponding weekdays of the previous year.
If one did not do Hatarat Nedarim on Erev Rosh Hashanah, he should do so during the Aseret Y’mei Teshuvah, or on Erev Yom Kippur. If one did not do Tashlich on Rosh Hashanah, he should try to do so during the Aseret Y’mei Teshuvah and if not he has until Hoshanah Raba. According to Nussach Sefard, Kiddush Levanah is not recited until after Yom Kippur, according to Nussach Ashkenaz, Kiddush Levanah is recited from the 3rd.