When I say “You are similar to him” I say Similis ei es. But when I want to say “You run like him” (similar to him) would that translate as Curris similiter ei? Or should I use the nominative instead of the dative when it’s an adverb?
similiter with dative is attested but rare. You have a whole range of options though, including pariter + dat. and various conjunctions: quomodo, velut, ut, tam… quam…, and others, often depending on what you are saying.
You can also use the same words that you know by modifying the structure of the sentence. For example, if you wish to avoid using similiter with a dative, instead of “You run like him”, you could say “You and he run alike”. There is a great deal of room for style in Latin 
Thanks for your reply!
yeah, although similiter with the dative isn’t especially common, it is a neat usage and is attested in mainstream classical authors, Livy (e.g.37.40.10), Pliny and Vitruvius all having examples. similiter ut is a more common means of expression, and I’ve come across it a few times in Cicero. even similiter atque can function thus.
~D