Were there plentiful surface deposits of stuff like iron, copper, etc and only after hundreds or thousands of years of easy pickings did "mining" need to begin?

In some cases, there were plentiful deposits of ore, and in some cases still are. But native metal (i.e., already in metallic form rather than as ore) is rare. Gold occurs as a native metal, but gold is rare. In some places, native copper can be (or used to be) found in useful quantities and sometimes in fairly large pieces. Native iron is rare, and in most places was mostly from meteorites.

Extracting metal from ore is the key step. The ores used are typical oxides (copper oxide, iron oxide, etc.) - if one starts with other ores (e.g., copper sulphide), they are usually converted into oxides by heating them in air (this process is called "roasting"). Once you have an oxide ore, you heat it with carbon, and the carbon will remove the oxygen from the ore and leave you with metal (typically, it's actually carbon monoxide, CO, and it grabs the oxygen from the ore to become carbon dioxide, CO2). This process, converting ore to metal, is called "smelting". Playing around with native metals won't teach you how to do this. It's thought that the path to discovering smelting was pottery, with accidental smelting of ores used as pottery glazes. Playing around with native metals will help you recognise that you've make little balls of metal, so then you might try again to make a larger amount deliberately.

/u/brigantus discussed the discovery of smelting in https://www.reddit.com/r/AskHistorians/comments/8538sf/how_was_metallurgy_specifically_smelting_casting/

Can softer metals just be hammered into shapes with rocks?

Yes, and even harder metals such as iron. Rocks are traditional hammers and anvils for iron-working in many places around the world. Sometimes iron hammers are used with rock anvils.

I discussed the forging of iron without using iron tools in https://www.reddit.com/r/AskHistorians/comments/7987zj/how_exactly_were_the_first_forged_iron/

Of course, once you're forging iron, then you can make iron tools. But given that sticks continued to be used as tongs, and rocks as hammers and anvils, even after it was possible to make iron tongs, hammers and anvils, shows that they do the job quite adequately.

Were there clay molds to melt and mold metal?

Yes. The harder part is to be able to get high enough temperature to melt the metal, at least for metals with high melting points. You can easily melt lead just over an open fire, but to melt copper, you want a serious furnace. Iron and steel? Much harder again, and in most of the world, casting cast iron ("cast iron" is iron with 3-4% carbon, and melts at a lower temperature than either pure iron or steel) is a relatively modern phenomenon, and casting steel is modern.

Is discussed some ancient casting technology in https://www.reddit.com/r/AskHistorians/comments/aebau0/how_were_smithing_tools_made_in_ancient_times/