Not well. Unlike most other countries in Asia, Malaysia has for a long time been a net oil exporter. Actually, it very recently became a net oil importer like most countries, and if that persists it will help Malaysia bear the shock.
Oil is a relatively inelastic good in the short run, which means that a 1% drop in oil prices leads to less than a 1% increase in demand, and so as prices fall, total revenues from oil fall. (This is not true of all goods; apples are relatively elastic, for example, so a fall in apple prices could actually bring more revenue to apple producers.)
Thus, when the price of oil drops, Malaysia's export revenues fall. With lower export revenues comes a higher trade deficit and a weaker currency. Unless the weaker currency brings in enough more export revenue to compensate, this will mean a lower standard of living for people in Malaysia, as their imported goods are now more expensive. (Imported oil will also be cheaper, however, which could offset this effect.)
Malaysia's government also directly uses oil revenue as part of its funding (a policy that is very much a mixed bag; it works well in Norway but not so much in Venezuela), so the loss in oil revenue means a loss in government revenue and therefore a higher budget deficit. Malaysia is a medium-sized country, so they are not so small that they have no power to control the value of their own currency; but they don't have nearly as much as a very large country like the US or China. While for the US a high budget deficit is practically just an accounting mechanism (nobody is worried about the stability of the US dollar; indeed, people are accepting negative interest rates to use it), in Malaysia it could become a real problem, and they might be forced to raise taxes or cut spending.
Yet, as we know from macroeconomics, such a policy would be contractionary---it would hurt the rest of the economy, and could push Malaysia into recession. Their best bet is to find ways of reducing the budget deficit that don't involve cutting useful spending or raising taxes; one thing that might help would be to cut subsidies to oil companies, which would raise the price of oil for Malaysian customers, but not any higher than it was before the global price plummet. Expansionary monetary policy is also a good idea; inflation shouldn't be a big problem since oil is such a big part of most prices (actually deflation might be, and printing money would fix that), and the potential for weakening the currency would hopefully be offset by the restored economic stability.
In the long run, Malaysia should diversify; it's never a good idea for a country to base its whole economy around a single commodity. They should invest in new industries so that in the future, bad news for one industry doesn't mean bad news for the country as a whole.