One of the difficult parts of Orthodox singing will be singing these melodies from text (usually at best pointed) on a printed page
I can't think of any way around having to memorize all of these tunes. An easy way to learn them is to sing one or two psalms a day  in the tone of the week to the appropriate stichera melody for a while. At the bottom is S. Rolando's chant guide.
 
 

 Stichera template tone 1                                 
 Stichera template tone 2                                   
 Stichera template tone 3                                    
 Stichera template tone 4                                   
 Stichera template tone 5                                   
 Stichera template tone 6                                  
 Stichera template tone 7                               
 Stichera template tone 8                                
 

Chant Guide