What you'll need: serum sodium, serum osmolality, urine sodium, urine osmolality.
1. Look at the serum osmolality. Since sodium is the major determinant of extracellular fluid's osmolality, a low sodium should be reflected by a low serum osmolality. If the osmolality is low, go to step 2.
If the osmolality is high instead, then you need to find the extracellular osmolyte that's sucking water from the intracellular compartment (thereby decreasing the sodium concentration). There are only two important causes here - glucose and mannitol.
If the osmolality is normal, then you may be dealing with a case of pseudohyponatraemia. This occurs when a solid is present in the blood in increased amounts. This solid takes up such an amount of space that there is less sodium per volume of blood. Examples of such offending substances are massively elevated triglycerides and the excessively elevated serum proteins that occur in Waldenström's macroglobulinaemia.
2. Look at the extracellular fluid volume. If it's increased (e.g. oedema), this implies that both sodium and water are excessively high in this patient (it's just that the water's increase outnumbers the sodium's increase here). The major diseases in this category are cirrhosis, cardiac failure, renal failure, and nephrotic syndrome.
If the extracellular fluid volume is decreased (e.g. the patient is dehydrated, or hypovolaemic) then sodium is being lost somewhere. If it's being lost in the urine, the urine sodium concentration will be inappropriately high (> 20 mmol/L). This occurs with diuretics and with hypoaldosteronism. If it's being lost elsewhere, the kidneys will try their best to hang on to any sodium, and so the urine sodium concentration will generally be less than 20 mmol/L. Such conditions include vomiting, diarrhoea, burns and even excessive sweating.
If the extracellular fluid volume is normal, then there are three conditions to consider: SIADH, hypothyroidism and Addison's disease. These can usually be easily distinguished with a few further tests (e.g. TSH).
3. Still no luck? If none of the above categories fit, check that the patient's urine osmolality is appropriately low (it should be less than 100 mosmol/L). If this isn't the case, consider whether it's possible that the patient is drinking (or receiving via IV fluids) more than 20-30 L per day. Needless to say, this isn't a common cause of hyponatraemia! However, if it ever does manage to occur, the amount of water taken in will exceed the kidney's ability to excrete it, and the sodium concentration will drop accordingly.
I think that the above schema is quite handy, but feel free to amend it to suit your own desires. Now, if you're feeling strong, click onwards and look at an approach to hypernatraemia.