Mining ore can be done with hands, but is much more efficiently done with a pickaxe. Mining speed is increased with each successive pickaxe upgrade (with the exception of the gold pickaxe which is slower than steel, but has other benefits).
Using gem pickaxes increases the yield. Like normal pickaxes, these benefits increase with progressively more expensive gem pickaxes. The life of gem pickaxes can be extended by only using them for the final strike; a normal pickaxe can be used until the block is nearly mined, then a gem pickaxe for the multiplier.
Gems are found in caverns. They are picked up by hand, not mined using a pickaxe with the exception of the gold pickaxe which can produce gems, ores, and time crystals with each strike. Since the gold pickaxe may produce bonus resources for each strike, using it only for the final strike (like with gem pickaxes) is only beneficial in prolonging its life, as it will not increase the yield.
The yield multiplier for gem pickaxes applies to time crystals, so the best gem pickaxe available should be used to maximize yield.