Dryness in prayer, is, in my opinion, actually a good sign. When you start to love God more, you have to start loving other things less. And when that happens, you start to feel the sadness of letting go of those things that are not God.
Now the fact that a man prefers the good of grace to all natural goods, the loss of which may cause sorrow, is to be referred to [the theological virtue of] charity, which loves God above all things. (St Thomas Aquinas, Summa Theologiae, II-II, Q. 136, A. 3)
Dryness in prayer is, at least in my experience, when I start feeling the sadness of letting go of things not God more than the joy of loving God. This is just natural and could even be preter- or supernatural, in reference to @TotallyCatholicTeen’s mentioning of St. Ignatius of Loyola’s discernment of spirits, by God withdrawing His consolation so that not only we can appreciate the price of loving Him, but to complete our letting go of the things that we have to let go.
Sadness is our souls’ way of processing the grief of letting go. If we want to let go of the things that hinder us from God, then we have to be patient and go through this sadness that is “dryness of prayer”.
So the tip for countering dryness of prayer is just keep on praying!