The Magid Meisharim (a malach who would speak with the Beis Yosef) told the Beis Yosef, "Today you completed your fortieth fast of consecutive days, corresponding to the forty days of the creation of a child. Although on many of those fasts you had pleasure from this world [which made the fasts imperfect, in accordance to the Beis Yosef's very high level]...nevertheless, since they were forty days and since they were during the weeks of Shovavim, they were accepted. Now it is (Yechezkel 16:8) דודים עת, a time of love."
This means that Hashem loves us on these days of Shovavim, and our afflictions, fasts, and any other means we use to attain forgiveness and atonement during Shovavim are accepted, even when these means aren't perfect and wouldn't otherwise be accepted throughout the year.
We don't fast too much in this generation because we are weaker than in the past, and fasts would weaken us and prevent us from serving Hashem properly, but we have other ways of attaining purity during Shovavim. During Shovavim, more minor and less perfect attempts for atonement will be accepted, even if they aren’t sufficient on other days of the year.
The Chayei Adam writes, "You shouldn't fast much. You should eat only the amount that you need to be alive. Don't eat at parties and keep Shabbos with all its details."
We don't fast, but we can eat properly by making brachos with kavanah, being cautious not to overeat, and avoiding harmful foods. If we aren't accustomed to eating this way the entire year, it is a siguf, an affliction that won't weaken us (it will only strengthen us) and will grant us purity in Shovavim.
Another example of siguf that we can do in our times is Taanis HaRaavad, which is to stop eating before ending the meal. This is a very difficult fast because the yetzer hara wants to continue eating. This purifies immensely.
Another counsel for Shovavim is to say Tehillim. The hint is that the last letters of (Shemos 1:1) מצרימה הבאים ישראל בני שמות ואלה spell Tehillim. (We read these words on the first Shabbos of Shovavim.)
Yet another area in which to improve is to study Torah without interruption.
These means will purify us immensely. During Shovavim, every small attempt towards taharah is significant and accomplishes so much.
