Experience and knowledge goes a long way but here are some pointers:
Agate, is it dyed? Agate naturally comes in many colours so it can be difficult to know if it is dyed or not. Dying the crystal takes away its natural beauty and also can affect the energy of the crystal. It does not enhance it! If you submerse the agate in water you should come to know pretty quickly if it is dyed as the colour will run. Another way of knowing if it is dyed is that, the majority of agate geodes come with a piece of rock attached, is the rock part dyed? Also the majority of agate has an aspect of white or clear quartz running through it, it is usually multi-coloured. Is it one uniform colour? If so it's most likely dyed.
Amber is very popular and so in order for people to cash in on this, a lot of amber is man-made. If you rub genuine amber vigorously off your clothing, the static build-up on the amber should be strong enough to pick up a tissue.
A considerable amount of turquoise sold is actually dyed howlite. Turquoise in its natural form is quite powdery so it is sometimes reconstituted and a resin is added to bind it. If the turquoise is sitting on a rock, you will know its real. Otherwise, check for large areas of brown and cracks in the turquoise as this is can be an indicator that it is genuine. It is very difficult to know for sure with this stone by just looking at it unfortunately. This ehow article has some good tips on identifying turquoise. Turquoise is relatively rare and can be quiet expensive. If it's cheap, it's most likely not the real deal.
Clear quartz and glass
I have seen in some shops, glass being sold on a pendant as clear quartz. Glass is generally lighter and clearer than clear quartz. Clear quartz can be very pure but more often than not, it includes cracks and inclusions. If a clear quartz piece is completely clear, it will be expensive. Quartz has a hardness of 7 and glass only has a hardness of 5.5 so glass will also become scratched more easily.
Sunstone and Goldstone
Goldstone is a man-made crystal and is known as 'goldstone' but some shops have tried to sell it as 'sunstone'. There seems to be some confusion. Goldstone can also be seen commonly in a blue format and is essentially a 'glittery' glass, whereas Sunstone is a beautiful, natural and iridescent crystal.Sunstone
Goldstone (image from wikipedia)
And so what about the crystals and minerals that are real but just look very alike? ...
Clear quartz and apophyllite clusters and points.
These two can look very alike but this one is easy. Quartz terminates into a point with six faces, apophyllite terminates into a point with only four faces.
Citrine and Golden Topaz
This one is very difficult as golden topaz being far more expensive usually comes in small packages and so compared with a small piece of citrine can be almost indistinguishable to the human eye. It's subtle but topaz is colder to the touch than citrine, so that can help if you just happen to have a piece of both to hand. Topaz is more expensive.
Citrine is heated amethyst. The citrine that forms naturally is amethyst that has been naturally heated in the earth. However, there is a massive amount of heat-treated citrine on the market. This citrine is very damaged and usually does not make for a good healing stone. The greater the contrast in the colour the citrine, the more likely it has been heat-treated.You can usually identify this type of damaged citrine as a very strongly coloured (almost brown) citrine sitting on a very white piece of quartz. Natural citrine is very dark (looks a bit like smokey quartz) and it is quite rare and more expensive.
Dyed or not dyed?
Bear in mind that some crystals are idiochromatic which means their colour runs throughout the entire crystal. If you were to grind these crystals down into a fine powder you would see a powder the same colour as the crystal.
Whereas some other crystals are allochromatic meaning that their colour is caused by refraction of light or inclusions. Amethyst is an example of such an allochromatic crystal. If you were to ground amethyst down you would find it creates a white powder and not a purple powder as you might expect.
The reason I mention this is because malachite, lapis lazuli and turquoise are all idiochromatic and for this reason they were used in the past for paint. You may find that if your fingers are wet, that some of the colour from these stones rubs off on you. This does not mean that they are dyed. This is another reason why turquoise is very difficult to identify.
The very definition of a mineral/crystal is that is has an inner, structured and repeating lattice. Oil and Gas are not technically 'minerals' they are 'hydrocarbons'. Water is not a mineral and yet ice is classed as a mineral because when water freezes it forms a crystalline structure.
There are a number of 'amorphous substances' (meaning non-crystalline) that are still used in 'crystal' healing. These include: amber (it is actually tree-resin, not a crystal), obsidian (which is volcanic glass), coral, mother of pearl, shells, petrified wood, jet and opal (opal is made up of spheres of quartz in water, which is why it would crack if placed in a dry, hot environment).
The only way to know for absolute sure what a crystal or mineral is, is to study it using special gem identification tools such as a refractometer.