Gluconeogenesis begins with various substrates converted into pyruvate, and this proceed though what is essentially the reverse of glycolysis (except for a few differing enzymes).
Many 3 and 4-carbon substrates can enter the gluconeogenesis pathway. Lactate from anaerobic exercise in skeletal muscle is easily converted to pyruvate; this happens as part of the Cori cycle.
Oxaloacetate (an intermediate in the citric acid cycle) can also be used for gluconeogenesis. Amino acids, after their amino group has been removed, feed into parts of the citric acid cycle, and can thus can generate glucose in this pathway.
Fatty acids cannot be turned into glucose, as they are broken down into the two carbon acetyl CoA. (However glycerol, which is a part of all triacylglycerides can be used in gluconeogenesis).