The first thing you should consider is that bilingual dictionaries are notorious for giving long lists of "meanings" or "translation equivalents" with little or no context.
Consider if you were learning English and wanted to learn the meaning of the word "set." You then encounter "sunset," "movie set," "jet set," "chess set," "set of tennis," "a set course," "waiting till glue 'sets,'" "a set-up," etc. What do you do? Two strategies tend to work: (1) pay attention to the collocations so that you can recognize the meanings even when they change slightly or are omitted and (2) try to establish a core meaning or meanings you can use to derive the others. In the case of "set," these are all things that "sit" or are made to sit together. This technique creates a reinforcing web of meanings that will help you even when you encounter new usages, i.e., a "set-piece play in basketball."
Two additional strategies that help in Mandarin are to recognize that sometimes one simplified character represents more than one traditional character with more distinct meanings. Usage can sometimes be complex, but sometimes you can associate the meanings with the additional character forms.
The other approach that works for me is to develop simple mnemonics that reinforce the meanings.
Here are examples:
To remember the core meaning of 得 (dé), I remember the etymology as “obtaining" something by taking strides 彳 to gain valuables 贝 that you handle with care 寸. For the use of 得 (de) in phrases like 说得好 ("speak well"), I just think of 得 (de) as a grammaticalization and reduced pronunciation of the meaning "obtain." "You speak so as to a obtain a result that sounds good." For 得 (děi), you can think of a mnemonic like: "to live one needs (得 děi) to obtain (得 dé) food and shelter.
To remember the "core" meaning of 干， I see it as sketch of a shield with a hand grip or a forked weapon or hunting tool. Use it for this rare meaning and for any loan usages where the syllable has no obvious meaning by itself, so 若干 (a certain number; how many/much) for both simple and traditional characters. Also use it for "concerned with" or "intefere," since shields 干 are concerned with 干 interfering 干 with someone trying to stab you with a forked weapon 干.
For 干/幹, you can look at the traditional character and imagine a simple mnemonic like: " during early morning 早 at court 朝 before the moon sets (i.e, take away the 月 element from 朝), people 人 would plant the emperor's flag on a post/tree/trunk 干 to show he was the shield (干) of the nation against calamity. For the various meanings of this usage, remember that "senior cadres/middle managers (高干/幹）and/or capable officials 干/幹员 do (干/幹) all the real work and are the backbone (骨干/幹）of any company you should not interfere (干/幹) with.
For 干/乾, 乾 is just the same as 幹, but with the flag drying 乾 as it flutters off the morning dew from the second 乙 it flies from the top of the pole or tree trunk 幹 . 乙 actually means "second in a series," and not a second of time, but looks like a winding/fluttering snake or a stream of water. You just show the flag flapping to get dry and drop the part that used to represent the pole 干 when writing the traditional character. The basic meaning is "dry."
干 (gàn, gān): to work, do, manage, tree trunk, to concern, shield, dry, clean, 干 has many meanings when its tone change