First of all, the Find Familiar spell clearly says:
a) a celestial, a fey, or a fiend; and
b) takes an animal form: bat, cat, crab, frog, toad, hawk, lizard, octopus, owl, poisonous snake, fish, quipper, rat, raven, sea horse, spider, or weasel.
From that, we can immediately infer that a pseudodragon cannot be summoned since it is a Tiny Dragon, which has a clear dragon shape.
Second, when they say "sought out by mages," it means the mages are searching for them, not conjuring them. This should be an adventure where the mage searches documents to find places where pseudo dragons live to have a chance to find one. For example, in Forgotten Realms they may only live in the wild on the Dragon Isle, next to the Pirate Isles in the Sea of Fallen Stars. It could also be a purchase from a place that knows where to capture them... but I have never heard of such a place!
That's the only way I know of to get a pseudodragon as a familiar. Also as explained in the MM on p. 254, the pseudodragons don't just accept a mage as their friend. They have to accept them as such and that could be another limit in having such a familiar: it could take quite a bit of work to make the pseudodragon not be scared of you, and then another bit of work to form the bound. It will depend on whether your players can accept such challenges too (mine are younger so I made it simple: give it food, it will be happy and come with you.)
As a DM, you could also limit the bound to only good characters (Since the dragon is neutral good.) However, D&D 5e does not really put alignments in such prospective so much. Yet, my players found a pseudodragon which was captured by an evil wizard and put in a cage. It never accepted to be bound to that wizard because he was evil...
Finally, the pseudodragon remains free and may leave at any time (maybe because it feels like it needs to mate, the characters are going to a place it doesn't want to go to, they stopped feeding him...)
In the end, though, you have a true familiar / pet while the bond lasts or the dragon is killed (a familiar from the Find Familiar spell is just a servant, in comparison.)
Note that when killed, you can of course apply the same rules as to your characters. So a cleric can bring it back to life with a Cure Wounds or even a Resurrection. Of course, a Resurrection is not cheap, but it may be way cheaper than searching for a new pseudodragon, especially because this one already accepted you and by restoring its life, you may create an even stronger bond!
The abilities offered by a pseudodragon are described in the MM p. 254 in the box Variant: Pseudodragon Familiar. If close enough, you can feel what the pseudodragon feels, you can communicate with it telepathically (limited to images though, since it does not speak) and you gain resistance to spells affecting you.
As a side note, you have many Conjure spells. You may want to read them all. As you will notice, none of them allow you to conjure a dragon (you could argue that conjuring a celestial would include the Bahamut, although it is way too powerful for the basic spell to work, it is a dragon... but I don't think that applies as such.)