Late to the party, I’m afraid, because of time zones. However, since more-or-less everything has been said already, I’m spared the chore of writing a treatise on chain sharpening… so, just to dot the ‘Is” and cross the ‘Ts”, and to emphasise some points…
There are folk who claim to be able to sharpen twist drills perfectly well by hand. Perhaps they can also do chainsaws, but ordinary mortals need help and guides.
Bill Phinn’s link (post #705653) to Stihl’s kit is exactly what you need. His earlier link (post #705608) is to a strange plastic and metal Stihl gizmo which, in my opinion, is near hopeless. My neighbour has one, and can’t use it; neither can I, so I end up sharpening his saw… I run four chainsaws here, from a pole pruner with a picco chain to a 72 cc MS381, the latter to deal with hefty eucalyptus trees, with up to 36″ diameter butts. The all-metal sharpening kits really work, and de-skill the sharpening process. The plastic and metal ‘gizmo’ takes too much metal off the depth gauges, and it’s difficult to see what you’re doing. Sharpen little and often – typically every three tanks-fulls (for abrasive eucalyptus, softwoods will be easier on the chain). I find that the (Vallorbe) files don’t last very long – the saw teeth are hard enough to snap. The all-metal guide allows you rotate the file to even out wear.
Oil reaches the chain through a very small hole in the side of the bar. There is no proper sealing, and oil can leak between bar and saw body quite easily. Make sure mating surfaces are clean! If the saw produces dust, it will find its way into the oil hole and block it, particularly if the chain is slack. As has been said, look for oil being flung off the end of the chain. If no oil, stop and fix it!
A sharp chain will run cooler than a blunt one, and collect less resin. Your pic suggests the chain has got pretty hot.
If the saw produces dust, it’s blunt! I can’t tell by feel or vision whether a chain is really sharp or not, but you’ll soon find out! It can be a challenge to sharpen each hand of teeth consistently, unless you’re comfortably ambidextrous. If wrong, the saw will cut a curved kerf. In the field, a chainsaw vice is more-or-less essential. You hammer them into a log, and can have a rest, sitting astride the log, bar pointing away from you, whilst sharpening.
Hope this helps.