Review the proper technique for fingering that scale. For many instrumentalists, this means ensuring that only your finger tips touch the keys or strings. Make sure the right fingers are on the right keys and that every time you practice that scale, you maintain the proper fingering, even while going quickly.
Move through the scale slowly, focusing on the tone of each note before moving on. Look for the quality of your voice and proper timbre of your instrument. Use the correct techniques for your instrument to make the timbre brighter or darker and keep you in control.
Play or sing the scale in a specific rhythm. Typically for one octave major or minor scales, the rhythm is 1 2 + 3 + 4 + 5 6 + 7 + 8 + 1. The rhythm you select depends on the kind of scale you select. Thirds are usually in straight eighth notes, some exercises require triplet rhythms and most vocal scale exercises have their own set of requirements.
Develop a routine for scale practice and warm up. Practice vocal scales by selecting one in the middle of your range and then moving up to the top of your range by half-steps and down to the bottom the same way. Many instrumentalists start at a C scale and move through the scales by fifths. Try this sequence of scales: C, F, B flat, E flat, A flat, D flat, G flat, B, E, A, D, G.
Use chromatic scales to incorporate more notes at the top or bottom of your range that you do not play or sing very often. Practice those sections often to make the transitions smooth.
Learn other modes aside from major and incorporate those scales into your practice and warm up as well. Try the Rough Guide to Musical Modes to help you learn more about them and what they are for. The more modes you play proficiently in any key, the more your musicianship improves.