In the diagram above, the input shaft is on the left side - the one with third gear on it. The left end of the input shaft extends out of the "front" of the transmission case. The clutch disk "rides" on the splines on the left side, and the end extends into the pilot bearing in the end of the engine's crankshaft. The output shaft extends to the right, and the end also extends out the "back" of the transmission case. The drive shaft attaches to the output shaft. The input shaft ends at the third gear in the diagram. The output shaft extends into a roller bearing in a "socket" in the end of the input shaft. This allows the output shaft to rotate independently of the input shaft even though they are in line. There is another shaft, the counter shaft, that runs through the counter gear.
The third gear is an integral part of the input shaft - machined out of one casting. The gears on the counter gear are usually one piece also (in the example shown in the diagram, the countergear is a one piece casting), although on some transmissions, the gears are independent but firmly attached to a splined shaft - in either case, all the gears on the counter shaft rotate together at the same rate. The reverse idler gear rides on it's own separate stub shaft and is used to reverse the rotation of the gears when shifted into reverse. The rest of the gears freely rotate on the output shaft. Note that all gears are constantly engaged, and whenever the input shaft rotates, all the gears also rotate. The synchronizers, however, are splined to the output shaft, and rotate at the speed of the output shaft. Actually, that's what turns the output shaft. In the case of the diagram shown above, if the engine was running, and the car was stopped, all of the gears would be rotating, and the synchronizers and output shaft would be stationary.
To understand how the engagement of gears (shifting), you have to understand the synchronizers. This synchronizer assembly is from a typical 4 speed transmission. I say that because this assembly has gear teeth along its outer circumfrence. They are straight cut, and are not in constant mesh with its opposing gear. Typically, the reverse idler gear is moved to a point where it engages the straight cut gear teeth on both this synchronizer assembly and the similar teeth on the countergear assembly. These straight cut teeth is why transmissions usually "whine" in reverse. Since the transmission pictured in the rest of the diagrams is a 3 speed, the reverse gears are keept in constant mesh like the rest of the gears, and reverse is selected using the synchronizer assembly and not a sliding idler gear. An exploded view of a gear, a synchronizer ring, and a synchronizer assembly is shown below:
The synchronizer ring (#7) in the diagram is what is normally called a synchro ring - it's the part that usually wears out. The synchronizer sleeve of the synchronizer (#1) slides back and forth on the synchronizer hub (#3), which is the part that is attached to the output shaft by he barely visible splines on the inner diameter. The synchro ring (#7) "rides" on the conical shaped part (#6) of the gear (# 5). When you shift into a gear, the synchronizer sleeve (#1) is moved toward the gear (#5). As it moves, the small teeth (#9) engage the teeth (#4) on the synchro ring, which causes the synchro ring to rotate at the same rate as the synchronizer assembly (#1 & #3) which are splined to each other as well as the output shaft. As synchronizer sleeve (#1) continues to move toward the gear, the inside of the synchro ring (#7) is pressed up against the conical shaped part of the gear. This causes the gear to match speed with the synchronizer, and once the speeds are matched, the synchronizer sleeve continues to slide toward the gear, engaging the teeth on the side of the gear.
The assembled synchronizer assembly:
The diagram shown below shows the operation of the synchronizer. The picture on the left is the position of the synchronizer when the gear is not selected. The next picture shows the movement part way throught the "shift". The synchro ring has been engaged, and is pressing on the gear, bringing the gear "up to speed", or in other words, synchronizing the speeds of the gear and the synchronizer assembly - why did you think all this stuff had the word synchronizer in it? Finally, the last picture shows the gear engaged. Note that the gear does not move to engage, the sleeve portion of the synchronizer assembly does the moving.
The diagram below shows the transmission in first gear. Note that the 1st-rev synchronizer (remember this is only a 3 speed) has slid forward to engage 1st gear. The arrows show the route of the power through the transmission. Third gear turns at engine speed, and drives the countergear. The counter gear drives first gear which is locked to the output shaft via the synchronizer. Second gear and reverse gear (via the reverse idler gear) are also driven by the countergear, but they are free to spin on the output shaft.
Same diagram show below, only with second gear engaged. Note the second-third gear synchronizer has slid back to engage second gear this time. Third gear turns at engine speed, and drives the countergear. The counter gear drives second gear which is locked to the output shaft via the synchronizer. First gear and reverse gear (via the reverse idler gear) are also driven by the countergear, but they are free to spin on the output shaft.
Third gear is shown below. Note the position of the synchronizers. The power is not actually "passing through" the gears, the synchronizer assembly has locked the input shaft to the output shaft, causing both to move at the same speed. Third gear still turns at engine speed, and drives the countergear. The counter gear still drives first gear, second gear and reverse gear (via the reverse idler), but they are free to spin on the output shaft.
This set up of locking input and output shafts was common in 3 and 4
speed transmissions. Then along came "over drive" 5 speeds.
In those transmissions, fourth gear was still usually accomplished
by locking input and output shafts together, but fifth gear was an over
drive - it just used another set of gears on the countergear and output
shaft, and another synchronizer assembly. The difference was that
the gears ratios caused the output shaft to be "over driven" - to be turned
at a higher rate than the input shaft - therefore the term overdrive transmission
was used (my '96 Ranger pickup still uses an "OD" on the gear knob pattern
instead of a "5" to show fifth gear).
And finally, reverse. Note that the power now passes through the
reverse idler gear to reverse the direction of rotation. The counter
gear drives the reverse idler gear, which drives the reverse gear which
is locked to the output shaft via the synchronizer. First gear and
second gear are also driven by the countergear, but they are free to spin
on the output shaft. Again, this transmission does not use straight cut
gears or a sliding idler gear for reverse.
Shown below is a exploded view of the Lotus Elan 4 speed transmission. The top "row" shows the input shaft on the left (with bearings), and the output shaft on the right (also with bearings). Notice the smaill roller bearing that is placed between them. The second row is the gears, bearings, and sychronizer assemblies that go onto the output shaft. Note that the gear (third gear which is about in the middle of the parts (from the left, second snap ring, sychro ring, and then the gear) goes onto the output shaft from the left side (up to the flange on the output shaft). The reset of the parts go onto the output shaft from the right. Note that in this transmission, the first-second sychronizer assembly (the part to the right of the third snap ring from the left) also acts as the reverse gear (like in the diagrams above showing the sychronizer functions). The third "row" is the countergear parts, and the fourth "row" is the reverse idler. In this transmission, the reverse idler is moved into position to engage the straight cut gears on the countergear, and the first-second sychronizer.
An exploded view of the Elan's transmission is show below. Note the shift forks on the left, between the case and the cover. They attach to the shift rods (next to the forks in the picture, and stick out the back of the transmission case. The other casing shown (the tail housing) bolts to the back of the transmission. The parts shown to the upper right, is the shifter assembly, and the "ball" on the bottom end of it sticks into the ends of the shift rods and moves them (and the forks, which move the sychronizer assemblies) forward and backward to select gears.
Hope this helps to understand the inner workings of the transmission...