Back in the day, it was easier to collect them all, because there were many kids who used to play those games, and you could find them anywhere. So it was easier to do the trades and complete your Pokedex in each game. But now it's almost impossible to find someone else. So you have to do it on your own. Here in this MyTake, I figured out a way, how to complete the Pokedex in each game on your own.
The first six Pokemon games (as you see below as well) are: Red, Blue, Yellow, Gold, Silver and Crystal.
Apart from those games, you also need: Another Game Boy device (Game Boy Color/Gameboy Advance/Gameboy Advance SP), and of course a Game Link.
So let's begin:
1) Start with a Charmander and a Squirtle in Red and Blue versions respectively. Once you do find a Pokemon center, trade Charmander in all other versions apart from Yellow. Do the same with Squirtle. Yellow has all the three starter Pokemon in Red and Blue versions, so it's not needed to trade them there. Repeat the same process, once your Charmander/Squirtle becomes Charmeleon/Wartortle and once again when it becomes Charizard/Blastoise. In Bulbasaur's case, it becomes available in Yellow after some point. Once you have Bulbasaur make sure to trade it in all other Versions, and repeat the process in its later evolving forms.
2) Likewise, in Gold/Silver/Crystal versions, start with a Cyndaquil, Totodile and Chikorita respectively. Trade Cyndaquil to Silver and Crystal versions, Totodile to Gold and Crystal versions and Chikorita to Gold and Silver versions. Repeat the same process once your Pokemon gets evolved each time.
3) Fossil Pokemon are not obtainable in second generation games. And in first generation games, you can only have either Kabuto or Omanyte. So make sure to pick Omanyte in Red and Kabuto in Blue, then trade them to the other version. Do it once again, when they evolve into Omastar and Kabutops. Also trade Aerodactyle to the second generation games.
4) Eevee is another special case. It has 5 different evolution forms (including those in the second generation games). This is the most complicated one actually. So here's what can you do:
Turn Eevee into Flareon in Red, into Vaporeon in Blue, and into Jolteon in Yellow. Trade Flareon/Vaporeon/Jolteon to other versions. Now in second generation games, try turning Eevee into Espeon in Gold and Umbreon in Silver. It's hard to achieve this though. Then trade Espeon in Silver/Crystal and Umbreon in Gold/Crystal, and you're done.
5) The three legendary birds (Articuno, Zapdos, Moltres) and Mewtwo cannot be found in second generation games. So make sure to trade them in second generation games as well. As for Mew...I cannot tell about this one. Haven't tried this notorious Mew-Glitch so far...but no problem, because Mew is an extra (and Celebi as well), so you don't need it in order to complete your Pokedex 100%.
6) Suicune can be caught in Crystal much more easily, instead of searching around. So once you do, trade it to the other two versions, so you will have only Raikou and Entei to capture. Although the legendary beasts are available in all three versions, it's suggested to catch them once, and then trade them to other versions. It will save much more time.
7) Another unique Pokemon is Hitmontop from the second generation games. Also you can only get Hitmonlee or Hitmonchan in the first games. So for example if in Red you get Hitmonlee and in Blue Hitmonchan, trade Hitmonlee in other versions, and do the same with Hitmonchan too. As for Hitmontop, it might be more difficult to achieve this, but do this at least once (in any version of the second generation games), and then trade it to the other two.
8. Apart from the unique Pokemon, there are Pokemon that cannot be found in all versions of the game. Yet they can be found, more than once. Here are those that cannot be found in each version:
Red: Sandshrew/Sandslash, Vulpix/Ninetails, Meowth/Persian, Bellsprout/Weepinbell/Victreebell, Magmar, Pinsir.
Blue: Ekans/Arbok, Oddish/Gloom/Villeplum, Mankey/Primeape, Growlith/Arcanine, Scyther, Electabuzz.
Yellow: Weedle/Kakuna/Beedrill, Ekans/Arbok, Raichu*, Meowth/Persian, Koffing/Weezing, Jynx, Electabuzz, Magmar.
Gold: Vulpix/Ninetales, Meowth/Persian, Ledyba/Ledian, Delibird, Skarmory, Phanpy/Donphan.
Silver: Mankey/Primeape, Growlith/Arcanine, Spinarak/Ariados, Gligar, Teddiursa/Ursaring, Mantine.
Crystal: Vulpix/Ninetales, Mankey/Primeape, Mareep/Flaafy/Ampharos, Girafarig, Remoraid, Octillery.
Judging by this, you can try to figure how can you "move", with the trades.
*If you trade an ordinary Pikachu in Yellow (and not Ash's special Pikachu), it can be evolved into a Raichu if you give it a Thunder Stone.
That's all. What you should be careful about, is to trade your unique Pokemon in each evolution form, because if you forget one then there's no chance you are going to capture the same Pokemon again..
Another thing you should keep in mind is, to have Pokemon from the first generation in the second generation games, as early as possible so you can do the trades. For example a Pidgey is the best option, because it's available very early in second generation games. It's also suggested to finish the first generation games first, BUT keep in mind to trade the unique Pokemon (Starter Pokemon, Fossil Pokemon, Legendary birds & Mewtwo and Eevee's first three evolution forms) in the second generation games, in each evolution form as well, so you won't miss them forever.