Interpolating in the mathematical or image analytic sense fits here. Free dictionary:

4. Mathematics a. To estimate a value of (a function or series) between two known values. b. To create a continuous function that incorporates (a finite set of data), such as creating a curve that passes through a fixed set of points or a surface through a fixed set of curves.
5. To introduce estimated values of (pixel data) into a pixel array to improve the quality of an enlarged digital image.

Unscramble:

1. to resolve from confusion or disorderliness
2. to restore (a scrambled message) to an intelligible form.

Source: Collins English Dictionary

It seems that the origin of the word is the impossibilty to reconstitute the egg once scrambled for an omelette.

Translating could apply to writing as well as speech.

Sounds like perspicacious

having or showing an ability to notice and understand things that are difficult or not obvious

Merriam-Webster

Construe /kənˈstro͞o/ verb –Google

interpret (a word or action) in a particular way.

I got lost on the way here! I was unable to construe the last line of his instructions.

Sue has a speech impediment, but fortunately for her, her husband and colleagues were very good at construing her speech when she was having a bad day.

To parse a phrase means specifically to understand or decipher a sentence, written or spoken. Strictly speaking the definition involves breaking a sentence down into grammatical parts, but I have heard it used more casually like this in practice.

Interpret /ɪnˈtɜr prɪt/ verb –dictionary.com

1. to clarify or explain the meaning of; elucidate
2. to construe the significance or intention of: to interpret a smile as an invitation
3. to convey or represent the spirit or meaning of (a poem, song, etc) in performance

Though I would define it in this context as: to analyse and conclude meaning from an ambiguous or otherwise unclear source.

I got lost on the way here! I was unable to interpret the last line of his instructions.

Sue has a speech impediment, but fortunately for her, her husband and colleagues were very good at interpreting her speech when she was having a bad day.

Am I the only one who thinks this is too obvious? Others have even mentioned it in the explanation of their answer, but not as the actual answer.

I'm almost certain the word you're looking for is discern.

Discern

I got lost on the way here! I was unable to discern the last line of his instructions.

Sue has a speech impediment, but fortunately for her, her husband and colleagues were very good at discerning her speech when she was having a bad day.

Elucidate

to make (something that is hard to understand) clear or easy to understand (m-w.com)

I would say follow, or grasp. It would help to know if this is a formal or informal word though, and whether you are looking for American, British or Australian English or generic.

Follow Collins dictionary

follow (ˈfɒləʊ)

Definitions verb

• to go or come after in the same direction ⇒ he followed his friend home
• (transitive) to accompany; attend ⇒ she followed her sister everywhere
• to come after as a logical or natural consequence
• (transitive) to keep to the course or track of ⇒ she followed the towpath
• (transitive) to act in accordance with; obey ⇒ to follow instructions (transitive) to accept the ideas or beliefs of (a previous authority, etc) ⇒ he followed Donne in most of his teachings
• to understand (an explanation, argument, etc) ⇒ the lesson was difficult to follow
• to watch closely or continuously ⇒ she followed his progress carefully
• (transitive) to have a keen interest in ⇒ to follow athletics (transitive) to help in the cause of or accept the leadership of ⇒ the men who followed Napoleon
• (transitive) to choose to receive messages posted by (a blogger or microblogger) ⇒ I've been following her online (transitive) (rare) to earn a living at or in ⇒ to follow the Navy
• See follow suit

Synonyms
= accompany, attend, escort, come after, go behind, tag along behind, bring up the rear, come behind, come or go with, tread on the heels of
= pursue, track, dog, hunt, chase, shadow, tail, trail, hound, stalk, run after,
= come after, go after, come next,
= result, issue, develop, spring, flow, proceed, arise, ensue, roll up, emanate, be consequent, supervene
= obey, observe, comply with, adhere to, mind, watch, note, regard, stick to, heed, conform to, keep to, pay attention to, be guided by, toe the line, act according to, act in accordance with, give allegiance to,
= copy, imitate, emulate, mimic, model, adopt, live up to, take a leaf out of someone's book, take as an example, pattern yourself upon
= succeed, replace, come after, take over from, come next, supersede, supplant, take the place of, step into the shoes of
= understand, get, see, catch, realize, appreciate, take in, grasp, catch on, keep up with, comprehend, fathom, get the hang of, get the picture
= keep up with, support, be interested in, cultivate, be devoted to, be a fan of, keep abreast of, be a devotee or supporter of

Grasp (ɡrɑ ːsp) Collins dictionary

verb

• to grip (something) firmly with or as if with the hands
• when intr, often followed by at to struggle, snatch, or grope (for)
• (transitive) to understand, especially with effort

noun * the act of grasping * a grip or clasp, as of a hand * the capacity to accomplish (esp in the phrase within one's grasp) * total rule or possession * understanding; comprehension

Synonyms
= grip, hold, catch, grab, seize, snatch, clutch, clinch, clasp, lay or take hold of
= understand, realize, take in, get, see, follow, catch on, comprehend, get the message about, get the picture about, catch or get the drift of
= grip, hold, possession, embrace, clutches, clasp
= understanding, knowledge, grip, perception, awareness, realization, mastery, ken, comprehension
= reach, power, control, range, sweep, capacity, scope, sway, compass, mastery

Mentioned by others in comments:
* Make out (two words) @user880772
* Comprehend @Elliot Frisch

Pick up is also a good but not one word

A casual usage word I used was make out.

to find or grasp the meaning of

to see and identify with difficulty or effort

(Merriam-Webster).

eg.

I couldn't make out his handwriting.

It was loud and I couldn't make out what she was saying.

Intuit would apply in a situation where the obvious connections in the language are invisible, yet can be internally or spiritually understood. This is the word I associate with my ability to accomplish a task using a sixth sense.

Just want to clarify, because I'm on a word hunt too. This font is far too small, and my vision is going, but im able to parse (is it parse?) What is written as i can make out some key shapes and extrapolate (extrapolate?) From the various recognizable parts and discern what has been written.

There's got to be a word for it. The ability to overlook typos and errors as you read at speed, not stopping to render (render?) Each word individually, but filling in details from context as you go.