The best thing is to upgrade some 2* champs to 3*, even if it takes some time.
There are other ways. Sometimes you get chickens as reward from quests (or you can buy them for real money). The chickens have stars like heroes and one chicken can replace one hero when you do an upgrade.
You could use ancient (blue) shards to get heroes of at least 3* and use them for your upgrade. But unless you are really sure wich champs are good and wich are not, you should be really carefull by sacrificing rare or better champs. Some people sacrifice their day 30 free champ High Khatun, definetly don't do that!
Skadi above explained it pretty much, but yeah, there's several ways to obtain champions to increase the stars of another one:
1- You can farm some rares 3* in the campaign, or you can level up the 1 and 2* until level 3 or 4 and use them as food
2- Opening shards is the best way to get champions. You can find all the info of what kind of champions and what rarity pressing the (i) button when in the portal
Some other champions are only obtainable by doing faction wars (Lydia) or the void tower ones. Arbiter and Ramantu are obtainable through progress missions and you also have the daily login ones. The hard part and the core of understanding the game, is understanding which ones are worth and which ones are useless