The context is the immediate surrounding text of the subject. For example, the central point of a parable would be solidified from the context of the teaching that Jesus was giving at the time he told the parable.
Using the word "flesh," it could be soft (in contrast to a stone) as in Ezekiel 11:19 (modern translations may have used a different word here); it could be man (human nature) as in John 1:14; it could be evil (a fallen human nature) as in Romans 8:5.
The Immediate Context
Frequently a word is defined in the context in which it is found.
Faith is defined by Hebrews 11:1-3; Perfect is defined by the context of James 1:4; Mystery is defined by the context of Romans 16.
Explanations made by analogy or antithesis analogy (explained by what it is not).
Covenant and promise in Galatians 3:15-17; Wages and gift in Romans 6:23.
Parallelism is a guide to the meanings of phrases. This is a common form used in poetry. Where we typically use rhyme in poetical structure, Hebrew uses parallelism to reinforce or contrast the meaning. Parallelism can more easily be translated because a properly translated word is not also required to rhyme.
See Psalm 112:1 and Job 3:1,3 for examples.
General reasoning or allusions of context help to determine or limit the meaning.
See "world" in John 3:16 and 1 John 2:15;
Irony or satire, meaning the opposite of what is said.
See 1 Kings 22 and 2 Corinthians 11 and 12.
Importance of observing parentheses or parenthetical thought breaks.
See Philippians 3:18-19 and Ephesians 2:2 through 4:1.
Be aware of hidden dialog -- change of person speaking or being spoken to without indicating change.
Examples in Romans 3, Isaiah 53 and 55, Psalm 91, and Song of Solomon.
The Wider Context
Consider the book as a whole. What are the tendencies the author is addressing, the spiritual quality, how well the author knew the recipients, the maturity level of the recipients.
For Galatians 5:4, see there other verses in Galatians: 1:6, 2:16, 3:3, 13, 19.
For Hebrews 6:4-6, see Hebrews 1:1, 3:1, 5, 4:14, 6:10, 7:11, 8:7, 10:23, 32-34.
Examine a particular section of a book dealing with that particular subject.
Example: Romans 1-2