First question: Are you asking about 5th edition, or the brand new 6th world edition?
But some generalities apply across editions:
Technomancers can do all the same matrix actions that Deckers do. Of course, since they don't use cyberdecks then they can't do the cyberdeck-specific things like swapping ASDF values or run cyberprograms, etc. But, if you want to throw a Data Spike, for example, the task is resolved the same way whether you're a decker or a technomancer.
Where Technomancers differ from Deckers (other than not using a cyberdeck) is they have access to Resonance powers. These parallel, more or less, the rules for magic. Complex Forms are basically "spells you can cast in the matrix" and Sprites are basically "Spirits that live in the matrix". The rules nitty gritty of course begins to get slightly different, depending on which edition you're playing.