As it has been said above, it partly depends on what kind of Pokémon you want to show the emotions of. Besides looking into the animals they are based off, there are some other ways you can show certain emotions, or levels of, depending on your setting.
However you don't have only the Pokémon itself to rely on, as social creatures as they are, it is a sure bet that they'll be interacting with the environment in some way to make sure their emotions are evident (if they want to make them evident, of course).
Gregarian Pokémon, I'm mostly thinking the ones based off of canids here, will probably express certain kinds of emotion by nudging each other in certain, specific ways. We know from the anime (not the best source, I know >_>) that mons like Pikachu will express certain emotions and social states (such as a welcome) by their readiness to cross tails. A Pokémon whose natural habitat is the caves or other enclosed spaces might react to a threat to their Trainer by assuming a body posture that "blocks" open access to them; this is easily doable with mons like Steelix or Excadrill. Pokémon like Salamence can be thought to consider their territory as everything they can survey when flying, so spreading their wings low and craning their neck to allow one to touch them can be interpreted somewhat safely as an acceptance or acknowledgement of friendship -- or of "Worthy Opponent"-ness. You can even take a page from some of the strangest behaviours of real life creatures, for example when a crow misses its partner, it "sings" its particular name repeatedly, as if trying to beacon it home; combine this with the ability of some other related birds to emulate varied tones - even those of human speech - for interesting emotional effect.
Inanimate or inorganic Pokémon are a bit harder to do, but you can still rely on their relationship with their environment to assist. Electric Pokémon as they are, Voltorb and Electrode likely have different buzz "tones" and frequencies to express different social states, probably a somewhat dull sound to merely announce their presence versus a shrieking sound to announce readiness to battle. Given their nature, Pokémon like Cryogonal or Litwick might be prone to clinging to a wall if they feel disoriented or threatened.
There is also the point of what you can do that looks "clear" most likely depends on what the source of the emotion is. If a Pokémon is trying to acknowledge another Pokémon's intentions or is enjoying what is clearly a great moment with its Trainer, and it can be shown more easily what the other member of the interaction is feeling, a convenient social shortcut is to have the Pokémon attempt some sort of imitation (if you have watched How to Train Your Dragon you might recall a particular scene showing how it almost works).
Last but not least, remember that Pokémon are not humans, and most certainly than not do not share the same scales or even scopes of what emotions to feel (if they do) or how to show them and up to what point (if they can). Use culturally-standar
d behavioural cues (such as scratching things as an indication of curiosity) or external cues (such as a Pokémon getting under its own Rain Dance to indicate sadness or depression) accepted for humans in as much as they could naturally do that, but be not afraid to just go ahead and have the Pokémon or someone else "tell" it if the signal feels like it could be incomprehensible to the other party. And be not afraid to switch the meanings of the cues around for some crosscultural teaching... after all, wouldn't a small personal rain be a thing that makes a Vaporeon feel actually happy? ;)