In many navies, including the USN to a point, the distinction between weight classes is very nearly arbitrary. In general, the smallest class of 'proper' surface combatant is the corvette. Next in line is the frigate, followed by the destroyer and then the cruiser. Above this lie battlecruisers and battleships. There are no battleships left in service, and no battlecruisers either except for the debatable example of the Kirov class, which most would call merely an unusually large cruiser. There are, however, some general guidelines.
Corvettes are quite small, between 500 and 2000 tons displacement. The distinction between a large missile boat and a proper corvette is very nebulous, however. Frigates are a bit easier to identify. They are almost without exception 2500 tons displacement or more, and usually armed for one main mission. In most cases, this one mission is anti-submarine warfare, though there are anti-aircraft frigates as well. Frigates tend to be long and very narrow, and often have a sharply raked bow, which places the anchors in a position where they won't strike the sonar dome. Most also have low, squat superstructures and a single mast, though two-masted frigates do exist. The US Navy's Oliver Hazard Perry class and the British Type 23 frigate are very good examples of the type. The Spanish Alvaro de Bazan, on the other hand, is not, being rated as a frigate but having the size and armament of a destroyer.
The exact cutoff between a very large frigate and a small destroyer is rather hazy, though in general, destroyers can undertake two missions, perhaps more, with equal ease. For example, the now-retired Spruance class destroyer was equipped for both anti-sub and anti-surface warfare, with anti-air self-defense capability. Other examples, like the British Type 42 or the Russian Sovremenny class are similarly multi-mission. Most destroyers are a bit broader in the beam than frigates and tend to have higher superstructures. Both single- and dual-masted configurations exist. Most destroyers are between 4500 and 7000 tons displacement, though more recent examples can be larger, often approaching 9500 tons as in the case of the Arleigh Burke class. Some newer classes, like the aforementioned Burkes, or the Japanese Kongo class, are fully multi-mission and verge on being cruisers.
The cruiser is an even hazier category, mostly because few examples exist. In general, cruisers displace upward of 10000 tons and are more heavily armed than a destroyer. Most are also fully multi-mission, able to undertake anti-air, anti-sub or anti-surface strikes, and most also have some land attack capability. There are four classes of cruiser still in service - the American Ticonderoga, the Russian Kirov and Slava and the Peruvian Almirante Grau. The Peruvian unit is a converted World War II-era Dutch light cruiser, and has no anti-aircraft missile systems, or any anti-sub armaments at all. She is something of an anachronism, and not typical of modern cruiser design. Of the remaining 3, the US type is a long, narrow-hulled dual-masted vessel with a large boxy superstructure. The Russian varieties are long, but broader with very sharply raked bows. Both Ticonderoga and Slava have two masts; Kirov, on the other hand, has only a single very large mack (mast and stack combination). All three are fully multi-mission, though the anti-ship missiles occupy much more prominent positions on the Russian designs. This is in large part because the SM-2 Standard that comprises the main armament of the Ticonderoga class was designed from the inception as a dual-purpose missile and that's only become more true with subsequent revisions. The Russian units employ separate launchers for every missile type and thus have a busier, more heavily-armed appearance, while the American type has a dedicated launcher only for the RGM-84 Harpoon missile, using its Mk. 41 VLS for everything else.
Gun armament used to be a deciding factor, but no longer is - the largest guns in use on any surface warship still in commission are Almirante Grau's eight Bofors 152mm/45 naval rifles. Besides these, the Russian AK-130 130mm/70 is the largest modern gun in use. Smaller weapons, typically 127mm, 114mm, 100mm and 76mm are used by most other navies, and are used on frigates and destroyers as readily as on cruisers. Most corvettes, and some frigates carry 57mm weapons instead. The Canadian Halifax class frigate (more of a light destroyer) is an example of this. Italy is the only nation which still routinely equips their ships with extensive gun armaments nowadays, though Russia's Sovremenny class destroyer, carrying four 130mm guns, is something of an exception. The forthcoming, but not yet constructed DDG-1000 class, also known as DDX, will feature two 155mm/70 heavy guns and two or four 57mm heavy autocannon as point defense, however.