##Haskell, 38 bytes

h%t|(a,b)<-span(<h)t=a++h:b
foldr(%)[]

The binary function % insert a new element h into a sorted list t by partitioning t into a prefix a of elements <h and a suffix b of elements >h, and sticks in h between them.

The operation foldr(%)[] then builds up a sorted list from empty by repeatedly inserting elements from the input list.

This is one byte shorter than the direct recursive implementation

f(h:t)|(a,b)<-span(<h)$f t=a++h:b
f x=x

Another strategy for 41 bytes:

f[]=[]
f l|x<-minimum l=x:f(filter(/=x)l)

Haskell, 38 bytes

h%t|(a,b)<-span(<h)t=a++h:b
foldr(%)[]

The binary function % insert a new element h into a sorted list t by partitioning t into a prefix a of elements <h and a suffix b of elements >h, and sticks in h between them.

The operation foldr(%)[] then builds up a sorted list from empty by repeatedly inserting elements from the input list.

This is one byte shorter than the direct recursive implementation

f(h:t)|(a,b)<-span(<h)$f t=a++h:b
f x=x

Another strategy for 41 bytes:

f[]=[]
f l|x<-minimum l=x:f(filter(/=x)l)