Since the previous answer didn't tell us much about what Trolls look like, I'll start with that. We are fortunate enough to have two drawings of Trolls by Tolkien himself; both pictures depict the trio Bill, Tom, and Bert, from The Hobbit:
As you can see, they appear to be large, humanoid creatures, muscular, but with pronounced pot bellies.
As for Orcs, they seem to have come in a variety of favors, so to speak. Here are some of the different descriptions.
The Orc named Shagrat, in The Two Towers:
In the red glare Sam, cowering behind the stair-door, caught a glimpse of his evil face as it passed: it was scored as if by rending claws and smeared with blood; slaver dripped from its protruding fangs; the mouth snarled like an animal.
[Sam sees] "his left claw clenching and unclenching feebly [...] and with his right claw drew out a long red knife and spat on it."
The full quote from Tolkien's letter #210:
“The Orcs are definitely stated to be corruptions of the ‘human’ form seen in Elves and Men. They are (or were) squat, broad, flat-nosed, sallow-skinned, with wide mouths and slant eyes; in fact, degraded and repulsive versions of the (to Europeans) least lovely Mongol types.”
In the tenth volume of The History of Middle-earth, in a chapter titled Myths Transformed, there is an essay on Orcs, which claims that Orcs were actually animals:
"The Orcs were beasts of humanized shape (to mock Men and Elves) deliberately perverted / converted into a more close resemblance to Men. Their 'talking' was really reeling off 'records' set in them by Melkor. Even their rebellious critical words – he knew about them. Melkor taught them speech and as they bred they inherited this; and they had just as much independence as have, say, dogs or horses of their human masters. This talking was largely echoic (cf. parrots)."
In the second volume of The History of Middle-earth, a different description of Orcs appears:
[The Orcs are] "...bred by Melko of the subterranean heats and slime. Their hearts were of granite and their bodies deformed; foul their faces which smiled not, but their laugh that of the clash of metal, and to nothing were they more fain than to aid in the basest of the purposes of Melko."
Appendix A of The Lord of the Rings describes the Uruk-Hai, one of the subsets of Orcs:
In the last years of Denethor I the race of Uruks, black Orcs of great strength, first appeared out of Mordor, and in 2475 they swept across Ithilien and took Osgiliath.
In his blog, "The Middle-earth and J.R.R. Tolkien blog", Tolkien scholar Michael Martinez describes the different kinds of Orcs:
For example, a Uruk of Mordor and a tracker are sent out to search for Frodo and Sam from the Tower of Cirith Ungol. The Uruk does not appear to match the physical characteristics of the Mordor Orcs led by Grishnakh who reinforce Ugluk’s Isengarders, who in turn do not resemble Grishnakh’s Orcs or the “northern” Orcs from Moria who had tracked the Fellowship as far south as Rohan.
The Uruks were the largest Orcs, and according to the Appendices in The Lord of the Rings they first appeared around the 24th Century of the Third Age. But they appear to have fragmented into multiple tribes, for the Isengarders called themselves “the Fighting Uruk-hai”, whereas no other Orcs referred to themselves as “Uruk-hai”. In fact, the Uruk from Cirith Ungol who tracked Sam and Frodo mentioned “a pack of rebel Uruk-hai” in passing, perhaps referring to the Isengarders (or, as some readers believe, to members of Gorbag’s company of Morgul Orcs).
Gorbag and Shagrat both appear to be Uruks but it is not clear how much they physically resembled each other. Shagrat was described as having long, loping arms and large fangs.
Sam and Frodo encountered another company of Uruks while moving through Mordor — these Uruks charge into a company of smaller Orcs with whom Sam and Frodo have traveled for a while. It is clear that the many groups of Orcs felt little loyalty to each other, even if they shared common ancestors. But Tolkien makes little to no effort to identify any sort of “tribes” among the Orcs.
Broadly speaking, we can identify Orcs of Moria (probably of at least two or more kinds), Orcs from Isengard (including the tall Uruk-hai and smaller Warg-riders as well as a third group described in “The Battles of the Fords of Isen”), the half-Orcs of Isengard, the Orcs of Minas Morgul, the Orcs of Cirith Ungol, the tracker Orc(s) of Cirith Ungol, the small Orcs whom Sam and Frodo infiltrate, and the Uruks who disrupt the smaller Orcs’ march on the road. Tolkien seems to imply there may have been dozens or hundreds of Orc groups scattered across Mordor, the Misty Mountains, and Mirkwood.
Wikipedia's entry on Middle-earth Orcs describes them as follows:
Orcs are described as ugly and filthy fanged humanoids. The largest can reach near-human height, but they are almost always shorter, and some are as small as Hobbits (since Frodo and Sam disguise themselves as such when they enter Mordor). In contrast, crossbreeds between Men and Orcs are called "man-high, but with goblin-faces." However, some Orcs are very broad, if not tall. Many Orcs have long arms, like monkeys or apes. Many of them also have crooked backs and legs.
The Uruk-hai of Saruman, exemplified by Uglúk, are shown to be physically different from the regular Orcs of Sauron. They are taller and have more human-like proportions while the latter are shorter and have longer arms (according to the description of Grishnákh). They also grudgingly tolerate the sunlight better. The Uruk-hai are different from most of the "Northerners", who came down from the Misty Mountains. These are said to be smaller than Grishnákh, who is "a short crook-legged creature".
Half-orcs are described later on by Meriadoc Brandybuck, who saw them marching out of Isengard, as "horrible: man-high, but with goblin-faces, sallow, leering, squint-eyed." The hobbits occasionally encounter unusual-looking Men such as the "ruffians" in the Shire, implying some of these might be half-orcs. During the scouring of the Shire it is stated that the ruffians that have invaded include half-orcs and more of the sallow-skinned, slant/squinty eyed folks like the Southerner spy.
And the invaluable Tolkien Gateway's entry on Orcs says:
In Tolkien's writing, Orcs are smaller in stature than Men. One "huge orc-chieftain" is "almost Man-high", but others must have been of a similar size to Hobbits (Frodo and Sam succeeded in disguising themselves as Orcs in Mordor). They had long arms and fanged mouths. Some had black skin. Some had short, crooked legs. They had black blood.
In its info box, the description of Orcs includes the following information:
Average height: generally around 3 1/2' or 4'
Skin color: Sallow, Green, Brown, Grey
Distinctions: Short, sallow
Tolkien Gateway's article on Uruks gives us a little more information about this specific race of Orcs:
They were faster than normal Orcs and could travel during the day without being weakened. They were not only faster but smarter, stronger and larger, though they were still shorter than Men.
They were all long-armed and crook-legged, not as tall as the Isengarder Uruks but larger than the Moria Orcs. They could see better in the dark than the Isengarders could.
They also appeared different physically: greater stature, swarthy, slant-eyed, thick legs and large hands. Although they did not like the light of the Sun, they could withstand it better than other orcs. Saruman promised them man-flesh as a treat.
If nothing else, all of the above information shows us that Orcs, although uniformly ugly and grotesque, were not monolithic in appearance. The only things that all Orcs seem to have in common are: horrible looking; discolored skin (variously described as green, black, sallow - that is, pale yellow - brown, or grey, depending on the individual Orc); short stature (even the biggest Orcs are not as tall as the average human); broad build; fangs; slant eyes or squint eyes; long, lanky arms; crooked legs (except perhaps in Uruks).