For most of the year this is a rather straightforward question.
Horned Larks show their distinctive black horns as well as a black mask, malar patch and throat.
Sprague's Pipits are rather a plain rich, light brown with pale legs and big eyes.
But in the summer things get a bit more tricky.
Young Sprague's Pipits look a lot like the adults with just a hint of a fleshy gape at the corner of their mouth, rather extensive buffy edges to the body feathers, pinkish bill, and big eyes.
The problem is that young Horned Larks often look very much like Sprague's Pipits (and other plain brown birds). Pyle (1996) states that "Juvs are very nondescript and might be confused with other species". He further states the the juveniles can be distinguished from "sparrows, longspurs, and other nondescript brown passerines" (probably as close as Pyle comes to saying LBJ's) by wing length, the length of the wing compared to the tail and "tasus laterally rounded (vs acute in most other species). None of these features can be readily determined in the field but one additional piece of information that Pyle provides regarding young Horned Larks is that the juveniles have "upperparts with white or silvery spots" and the bill is somewhat conical. Horned Larks molt out of the juvenile plumage by August (or earlier depending on when they hatched) and look like a very pale, washed out version of an adult for the rest of the year.
Below is a series of photos of young Horned Larks (one of these may not be my photo but I can't remember who it might belong to so if it is yours please let me know).
The two photos above depict Horned Larks in their juvenile plumage. Notice the all dark back with white specks. The top of the head and the neck have the same pattern as does the feathers at the bend of the wing. The legs are pale but not nearly as pinkish as the pipit. The bill also looks thicker at the base on the larks and one thing I have noticed in these photos is that the lark's bill looks very plain grayish brown, whereas the pipits bill has a strong pale or pink tone.
The photo above depicts a young Horned Lark later in the season, mostly molted out of the juvenile plumage into the hatch year plumage. The black with white speckled feathers on the back and wing are mostly gone, making the bird even more brown and similar to the pipit. However, the same molt has also introduced more distinctive facial markings on this bird, helping to distinguish this bird as a Horned Lark.
So what is depicted in the photo below (photos taken June 24, 2010) ?
From this angle it is certainly rather plain and brown. The legs are pale, but not bright pink. The back of the head is rather plain and dark with no streaking. Notice the color and pattern of the back. It is rather dark with white or silvery spots.
It gets a bit easier when we get a look in profile. Notice the face is beginning to develop a bit of the adult Horned Lark pattern - a dark mask, cap and malar patch. The bill is rather drab and gray with just a hint of pink. Also note the color and pattern on the pattern on the lesser and median wing coverts - dark with some spotting.
When viewed head on the horns even seem to begin to be suggested. Otherwise the bird looks very plain although the breast looks to have rather diffuse spots rather than the streaks you would find on a pipit (see the photo above).
Note the Spragues Pipit above. This is a hatch year bird with rather broad buffy borders on the back and wing feathers (as compared to the after hatch year bird singing in the photo above). The eye looks large, there is a richer brown color to the plumage (particularly on the face), the bill is strongly pink, and (although not readily apparent in this photo) the legs are bright pink, and the bill does not appear conical, but rather long and thinner than a Horned Lark.
Pyle, Peter. 1997. Identification Guide to North American Birds: Part 1 Columbidae to Ploceidea. Slate Creek Press. Bolinas CA.