Doubling a melody in thirds or sixths is one of the nicest ways to spice up a texture. There are lots of different ways of doing it as shown in the examples below.
The simplest way of using thirds or sixths is for the texture to consist just of a pair of instruments playing these intervals. In the extract below, the violin plays a simple descending sequence first joined by the second violin in sixths and then the viola (which has a lower range). In this sort of texture you don’t need to worry too much about the chords implied as it all sorts itself out pretty much.
Haydn String Quartet Op. 33 No. 3, fourth movement
Earlier in the same movement, Haydn presents his main tune in thirds on the second violin and viola. This time the first violin joins in with what is effectively a decorated pedal:
Another way of employing thirds or sixth is to use them to thicken up a texture rather than, for example, using repeating chords.
In this Mozart string quartet the second violin mostly doubles the first in thirds while the cello plays the bass note and the viola fill in.
Mozart String Quartet KV 157 I: bb. 1-8
You have to be careful in this sort of texture that the added thirds or sixths fit with the harmony (they should follow the same dissonance rules as any other melody). It is worth trying thirds and sixths to see what works best. You will probably need to change the odd note that does not fit, so at the beginning of this example, a third below (an A) would clash with the C harmony, so Mozart just starts with them in unison.