себе This is a so-called “ethical dative” or “dative of interest,” and serves as a colloquial way of emphasizing that the subject did something for his own purposes. An English counterpart might be that “they lived alone, minding their own business.”
да In addition to its familiar meaning of ‘yes,’ да is also used as a colloquial equivalent of и. Note the somewhat corny folk saying about the modest food of Russian peasants: Щи да каша, пища наша ‘Cabbage soup and kasha are our food.’
овдовел Note the root вдов-, cf вдова ‘widow.’ The prefix о- indicates a change of state, cf. оглох ‘became deaf’ (глухой), онемел ‘became mute’ (немой).
мачеха ‘Stepmother.’ Note the root ма(т)-.
извести ‘Destroy’ or (less decisively) ‘torment.’
Раз отец уехал куда-то, мачеха и говорит девочке Note that the narration shifts at this point from the perfective past tense into the historical present, as is also common in story-telling in English. This shifting of tense is used elsewhere in this story, as well. The use of и here is emphatic. One might translate the phrase along the lines of ‘… Once when the father had gone away somewhere, the stepmother up and says to the girl … .’
Поди A colloquial alternative to пойди.
иголочку и ниточку Note the diminutives: ‘little needle,’ ‘little thread.’
тебе рубашку сшить The dative тебе here is the subject of сшить, so that the phrase means ‘in order for you to sew a shirt.’
мне рубашку сшить See the note about тебе рубашку сшить, above.
Та ‘That one’ = ‘she’ (the girl’s aunt). Тот or та are frequently used to indicate a change of subject.
и See the note about мачеха и говорит девочке, above.
племянушка ‘Niece.’
стегать ‘Whip, lash.’
подлей им под пяточки маслица Подлей is the imperative of подлить ‘pour under.’ Пяточки = ‘hinges.’ Маслица is a partitive genitive, indicating ‘some oil.’ The whole expression thus means to pour some oil under (that is, inside) the hinges, and it uses a dative pronoun (literally “pour some oil for them under the hinges”). Note the diminutive маслица here and хлебца, immediately below.
будут рвать Literally ‘tear,’ but the imperfective here indicates that the dogs will behave threatening, rather than that they will succeed in harming the heroine. The same is true of the scratching cat, below. The technical term found in grammar books for an imperfective that means ‘attempt to do something, but not necessarily succeed’ is “conative.”
хлебца See the note about маслица, above.
будет глаза драть See the note about the threatening dogs, above.
ветчины Partitive genitive: ‘give him some ham.’
идет, идет Comparable to ‘she walks and she walks.’ Note the change of tense twice within this sentence; perfective past verbs get her in motion and mark her arrival at her destination, but the motion in between is described with a historical present.
хатка Dialect equivalent of изба, избушка.
покуда A colloquial version of пока ‘while.’
кросна ‘Loom.’
решетом ‘Sieve.’
гребешок ‘Comb.’
полотенце ‘Towel.’
широкая-широкая Repetition of the adjective is a common colloquial way of expressing intensity, e.g., ‘very wide.’
давай бить Literally a hortative (‘let’s beat’), but here indicating that she ‘up and started to beat.’
колотить A synonymn of бить.
горелой корочки ‘(Not even) a burnt crust (of bread).’
ступу ‘Mortar.’
толкачом погоняет ‘Urges herself along with a pestle.’
помелом ‘Broom.’ The standard Russian word is метла, and помело is used mainly as ‘mop’ or, as in the present case, ‘witch’s broomstick.’
да и Да и, like simple да, is a colloquial equivalent of standard и.
дочиста An adverb built from the prefix до- and the root чист-.
дремучий ‘Dense.’ This is the traditional epithet for forests in folklore and poetry.
прогрызть Note the contrast between the preceding imperfective, which indicates participation in an activity (“she started to gnaw at”) and the perfective here, which focuses on completion (or, in this case, the lack thereof: but she was not able to accomplish the act of gnawing through).