Standard Picking
Standard picking is the most valuable technique when playing a basic solo. Standard solos don't require excessive picking speed; they instead need a simple down picking motion, or an up-and-down motion. When moving from one fret to the next on your guitar at a moderate pace, picking the string in a simple down motion will suffice; however, when playing more rapidly or when switching strings, playing with the bottom of your pick then switching to the top, allows you to access the next note faster.
Pull-Off
More than just your pick can help you play a solo. You can also pick with your fretting finger. For example, when playing a note with your first finger on the first fret of the first string, you can play a note by placing your third finger onto the third fret of the same string and picking with the opposite hand. Then you can pull off with the same finger by bending your finger to slightly grab at the string then releasing it to make a sound. This provides a quick way to play the first string of the first fret again in the example.
Hammer-On
A hammer-on involves the use of either a finger from your fretting hand, the pick or finger from your opposite hand, or both. When playing a note, hammer your fretting finger onto a string that is higher than the note you are playing, but within reach. Then, like a pull-off, you pull the string with your finger then release it. You may also hammer your finger or pick from your picking hand on a fret then do the regular hammer-on pull-off with your fretting hand, which was described earlier. Time the order so that the picking hand hits the string and pulls off first, followed by the finger on your fretting hand.
Practice
Effective solo picking techniques involve a great deal of timing, which can only be achieved through practice. When developing your technique regularly, you will develop calluses on the tips of your fretting fingers, and on your picking fingers if you use them for your hammer-ons. Calluses will help you develop crisp sounds when using your fingers to pick notes and when you are playing basic open notes.