Before and during practice, take the effort to understand, to "get" the feel of a song. Mechanical as it sounds, playing an instrument involves a substantial amount of coordination and muscle memory. Make the task easier for yourself by developing a mental sequence of sorts. A kind of, you know what comes next, mental programming.
It also helps if you have a firm understanding of basic musical concepts such as scales, chords, the Circle of Fifths, etc. Music is highly mathematical, in the sense "certain things" always happen with certain other things. For example, a D-Minor bar will almost always contain the notes of the D-Minor chord. Over time, such understanding develops a natural anticipation of what to play. In other words, you don't need to rely on hard memory or sight reading all the time.