If you practice frequently and for more than an hour at a time, you will be able to build up decent finger strength on your own. But if you're looking to quickly build finger strength and stamina, there are an unlimited number of exercises you can do to speed up the process. Most finger exercises are mentally challenging as well, which adds a second degree of practice. The following samples are exercises that sound horrible but yield great results if used actively. The purpose of these exercises is you help your mental skills and your physical finger skills.
The best way to get quality practice time in is to practice your scales up and down. Start with a simple major or minor scale and play it up and down without stopping for about 5 minutes. While you're playing, focus on making clear, crisp notes and keeping both hands in time. Also focus on how the scale feels and sounds. Make sure your fingers are fretting the notes correctly, between metal frets. Keep your fingers down on the fretboard until you have to move them to a new string. When you move to a new string, don’t lift your fingers off the fretboard farther than you have to. This is a very common mistake in brass horn players and can happen to guitarists as well. Only move your fingers as far as you must so you can avoid wasting time moving your fingers farther than you have to. With ALL of these points in mind, let's move on to the next exercise.
This is a popular John Petrucci riff that can take you a long way. This exercise can also be used on both acoustic and bass, maybe even more effectively because of their higher string gage. The shape used in the exercise is like a staircase that is inverted several times. Each time you play the shape once normally and once inverted, then you move it up one fret and continue. Make sure to keep your fingers on the fretboard as long as possible, and let the notes ring out the best you can. Keep the whole exercise flowing and moving. Start off slowly and pick up the tempo gradually as you feel more comfortable. Don’t focus on making the shape and then playing, but start playing the shape before all of your fret fingers are all the way down. It’s the best way to keep everything flowing smoothly. This exercise will greatly help your finger accuracy and speed.
Another great exercise is the chromatic scale, or any chromatics for that matter. Running up and down the chromatic scale can help speed, accuracy and of course finger strength. Do this often to keep your fingers synched up. And of course, if you have some favorite guitar solos with long eighth- or sixteenth-note runs, you can practice them over and over as well.