Aliens themselves would probably be built so different from ourselves that we'd have trouble recognising them as living things, let alone see them as conscious beings, or even empathising with their ''feelings''.
Well, if you think about it, it's quite probable they'd be similar to us, at least to some degree:
1) They'd be made from the same elements, and it's a reasonable assumption that they'll be carbon-based as well - it's rather hard to form carbon-free polymers, and you kinda need polymers. From this follows that they'll be active in a similar temperature range, and that they'll have pretty much the same basic needs as us. Given that we're thinking about a rather active being, it's further reasonable to assume that they need to breathe.
2) They'd be intelligent, so they won't be tiny (I heard a guesstimate of 10cm as the lower bound for intelligent life); 1) implies that they won't be overly huge, either.
3) They'd manage to reach us, which implies technology, which indicates a social creature, which means they'll show some of the same basic behavorial patterns as us. The number of genders is anyone's guess, but I'd expect two, or at least hermaphroditism - more and it's unnecessarily complicated, less and you get problems with evolution and stuff. There's a reason there's so few asexual animals/plants, and that so much energy is expended on mating behaviour.
4) They'd be capable of innovation (see 3) ), which means that each individuum must be of a rather high intelligence - an anthill will never use tools, and true hive-minds are impossible because of the need for communication between the single units. That high level of intelligence means that the population density must be low-ish to avoid starvation, which means the (original, natural) social units must be small or medium-sized, just like with humans - which implies a psychology that is at least not completely alien to us.
Please note that I'm not talking about the details of their shape, biology, sociology etc. - I'm just trying to do broad deductions and show that they'll be more similar to us than you might think.