Start by having a bird guide. If you have one already, spend a bit of time looking it over to recognize characteristics of some basic bird groups (sparrows, fnches, thrushes, chickadees, blackbirds, etc.)
To try to identify a specific bird you've seen, look for general shape, size, colours (which colour where), beak shape, eye brows, eye rings, wing bars, tail lengths and markings etc. Try to narrow it down to one of the groups, like those mentioned above, and then start scrutinizing the likely contenders based on some of the more subtle details mentioned in the guide. Pay attention to geographic location and habitat. Consider behaviours (walking vs hopping, ground bird vs tree tops, bobbing tail, stationary vs constantly moving)
As for your bird, if it had a thick beak, then look for finch types (house finch, purple finch, female cardinal). If the bill was narrow and the bird was reddish brown rather than brownish red, then perhaps it was a thrush (veery, hermit thrush)
Hope that helps for a start.
Scott