ましょう is one of the conjugations of the
auxiliary verb ます, and is a common (polite) way to suggest that something be done 'together' (when used with a verb). It is often translated as 'let's (A)', or 'shall we (A)?'. To use
ましょう, we will simply need to change ます to
ましょう, when conjugating the verb.
Despite regularly being translated as 'shall we (A)?',
ましょう does not specifically target another person, and can also be used as a declaration that (A) will be done/needs to be done. This use reflects the base meaning of
ましょう, which is the polite volitional form (deliberately/purposefully doing something).
In this example, the speaker is expressing to themselves that they 'will' do something, and are strongly resolved to make it happen (similar to 'I shall' in English).