If one of your objectives is to gain as many points as possible, the conservation of energy is your priority; upon the completion of each mission, your remaining energy figures into the score. Points are also added for each piece of candy you've given to Elliott (during the "kissing" animation), so your second score-related concern is that all pieces are handed over before the spaceship is called.
Your counterpart -- E.T., of course -- should continually walk at his normal speed, rushing only when escape is required from either of his adversaries; fast movement uses up proportionately more energy over identical distances.
Up to nine pieces of candy can be held at once; when these have all been collected, find the symbol pictured here and press the button. Elliott will eventually walk up and take the candy. Nine more pieces can then be picked up. If you've given Elliott a full batch, avoid calling him when you're holding none, or he'll bring you one of the unclaimed phone parts in exchange (assuming that any remain). Consequently, the points for those last nine pieces won't be awarded at the end of the mission.
As you encounter arrow symbols, try to commit their locations to memory. When the F.B.I. Agent or Scientist is hot on your green heels, teleporting to an adjacent screen is a less costly means of escape than accelerated travel. (Teleporting uses up more energy than merely walking to the same destination, but still not as much as running.)
The only problem with teleportation is the possibility of falling down a well that's located at the same position on the destination screen as the arrow. A better way to get rid of either rival is to keep walking (your normal speed is identical to their only speed) until you find the zone whose symbol is seen here, duly pressing the button to activate it; this will trick your foe into returning to the city screen.
On his way there, he'll almost always be obstructed by the southern border, valiantly walking in place -- but posing no danger in collision -- until another human enters the screen. This makes your exploration less complicated for a little while, but it prevents you from activating the Spaceship Zone, should it be on the same screen as the blocked enemy when you're ready to call the ship.
If you've fallen down a well, immediately press the fire button to halt in midair, preventing the energy loss that results from impact. If part of the phone lies at the bottom (or you'd like to pause the game by remaining down here), drift downward until you land. Otherwise, levitate from the well without delay; energy is constantly expended while you're floating.
This zone should never be activated if you're taking the score into account. If the conservation tips above are exploited, you won't have to eat candy for more energy; you'll be able to give every piece to Elliott. Before calling the spaceship, ensure that you've revisited every screen containing wells, confirming that no further candy has been provided.
Remember that using this zone reveals only one part of the phone. If the same screen harbors another piece, you won't know until the first has been taken (or you happen to fall down the correct well); so revisit the question mark after grabbing the phone part, just to be sure.
Once you've collected all three phone pieces (and given all available candy to Elliott, if you're playing for score), walk northward to the forest screen, and commit to memory the sites of its City and Landing Zone symbols (the latter is seen here). Now find and activate the Spaceship Zone. Finally, return to the forest, stand in the City Zone and wait for your pursuers. There can be only one human on the screen at a time, so they'll arrive individually. Each will have to walk all the way from the city screen located far to the south...
...because all humans return to the city when you activate the Spaceship Zone (whose location should obviously be remembered if you find it prematurely, so you won't waste energy by searching for it after the phone's been assembled). Neither the Agent nor the Scientist should be present in the forest when the ship-landing timer finally ticks itself out, as every human but Elliott will scare away your rescuers, obliging another visit to the Spaceship Zone, and reducing your energy accordingly.
So the instant each enemy walks into the forest, activate the City Zone. The duration between each of their visits is fairly regular, as they're never blocked on the way southward from the forest. Immediately after casting out the third bad guy, rush to the Landing Zone symbol -- it can take a second to find the precise spot -- and wait to get rescued.
E.T. has four Easter eggs: more than any other VCS game. The secret with no connection to the others is found only in Game Variation 1. Give Elliott a single piece of candy; whenever you're both subsequently on the screen that bears eight wells, graphic artist Jerome Domurat's initials appear at the top.
Unveiling the other Easter eggs involves completing two missions in a row. Game 3 is recommended, as the Agent and Scientist actually stay at work all day. As seen at the bottoms of wells (rather than in your inventory), the phone pieces are roughly shaped like programmer Howard Scott Warshaw's initials. After starting a new game, search until you find the piece shaped like a skewed H.
Now give Elliott seven pieces of candy. It actually doesn't matter whether you do this -- nor how much of that candy you collect -- before or after taking the phone part, as long as exactly seven pieces are relinquished at one time. Now search for and revive the flower, which will promptly take wing as a Yar (giant mutant housefly) from the game Yars' Revenge.
While only the piece shaped like an H is necessary for bringing this Easter egg to light, you can possess the other two as well; in fact, if you can't find the flower, one of them might be covering it up, in which case it won't be visible until you grab the phone piece and then plunge into the well a second time. For this reason, you might as well pick up any other pieces that you stumble upon; you'll need them for getting yourself rescued anyway.
After the mission has been completed and the score has been calculated, press the fire button to embark upon a second mission. This time, the required phone part is shaped approximately like an S.
Once again, give Elliott seven pieces of candy and restore the flower. As it turns out, you've resuscitated Indiana Jones, hailing from the game Raiders of the Lost Ark and apparently having reached an especially unremarkable point in his explorations.
In the third mission, the only essential phone piece is shaped like a W turned on its side.
When the flower has been revitalized this time, part of your energy readout is obscured by the final Easter egg: Warshaw's initials. The number indicates that this is the third VCS game he's written; the characters embodying the prior eggs feature in the other two games.