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 (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
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