There are a lot of overly complicated ways to insert a line after every nth line, but the simplest way I find is the following:

sed '0~3 s/$/\nMy Text/g' < input.file  

In a file with six lines you get something like the following:

Line 1  
Line 2  
Line 3  
My Text  
Line 4  
Line 5  
Line 6  
My Text  

Just swap the second half of 0~3 with the number of lines after which you want to insert to adjust where you insert your text, e.g. 0~30 will insert every 30th line.

The first digit of the 0~3 specifies the first line the insertion should happen (with 0 not prepending to the beginning of the file):

sed '2~3 s/$/\nMy Text/g' < input.file  
Line 1  
Line 2  
My Text  
Line 3  
Line 4  
Line 5  
My Text  
Line 6  

To insert something every nth character the syntax is a bit different:

sed 's/.\{2\}/&#/g'  

Will insert a # every 2 characters:

Li#ne# 1#  
Li#ne# 2#  
Li#ne# 3#  
Li#ne# 4#  
Li#ne# 5#  
Li#ne# 6#  

Swap out the 2 for the desired number of characters.