There are other Idealisms besides Berkeley's but I will concentrate on Berkeley since the question centres on him.
Other minds - a crux in Berkeley's theory
Berkeley has little to say about our knowledge of other minds - specifically, about why he is entitled to suppose that there are other minds besides his own. God is an exception since Berkely is sure he can deduce the existence of God.
Knowledge of other minds poses special problems for Berkeley. Besides taking the bodies of other persons to be mere collections of
ideas in my mind, he insisted that I cannot have any idea of the mind or
spirit of another. For him, ideas are passive and inert and therefore totally
inadequate to convey a likeness of an active being, spirit, or mind (Principles 21) Lacking ideas of minds, Berkeley supposed that I can still come
to know of my own mind through a peculiar non-sensory capacity, which
he called "inward feeling or reflection" (Principles 89), and that I can
deduce the existence of God by reflecting that only a supremely wise and
beneficent spirit could produce the variety, order and coherence exhibited
in my ideas of reality (Principles 30). But while he prided himself on having
provided a clearer and more certain proof of the existence of a divine spirit
than any other in history (Dialogues II 212-213), he had little to say about why I should suppose that other minds than mine exist.
But he is not without resources:
The primary locus for Berkeley's views on other minds is Principles 145:
From what hath been said, it is plain that we cannot know the existence of
other spirits, otherwise than by their operations, or the ideas by them excited
in us. I perceive several motions, changes, and combinations of ideas, that
inform me there are certain particular agents like my self, which accompany
them, and concur in their production. Hence the knowledge I have of other
spirits is not immediate, as is the knowledge of my ideas; but depending on
the intervention of ideas, by me referred to agents or spirits distinct from my self, as effects or concomitant signs.
Argument from analogy?
No, for the following reasons:
It has frequently been maintained that the argument of this passage is one
from analogy. Supposedly, Berkeley appeals to a certain resemblance be
tween our ideas of our own bodies and our ideas of other bodies and from
this he infers that other minds exist.2 But the argument for other minds
that is contained in this passage is not an argument from analogy. Berkeley
does not say that we infer the existence of other spirits from a resemblance
between their bodies and our own body or even from a resemblance between
their operations and our own operations. He simply says that we infer the
existence of other spirits "from their operations." There are no premises
affirming likeness or similarity or resemblance between these operations
and any other. Berkeley does indeed note that these finite spirits, whose
existence he infers, are "like myself." But this is stated as a conclusion, not
as a premise.
Argument from causation
This appears to be Berkeley's main argument.
While Principles 145 and 148 do not appeal to analogy they do appeal to
the cause-effect relation. In Principles 145 Berkeley refers to the ideas I
have as "effects" which are "excited in us" by other spirits or "agents" which
"concur in their production." And in Principles 148 these other spirits are
described as "principles" of thought and motion. The idea is clearly that
from the changes in my ideas - particularly those which I take to be
expressions of thoughts or motions of a body - I go on to infer the existence
of a particular cause responsible for those changes. This cause I then take
to be another spirit, incidentally like myself. Another spirit because, as
Berkeley frequently insists, spirit just is the only possible cause. And like
myself because, presumably, the effects I witness are limited to the
thoughts and emotions of some one animated body (hence the spirit is
another finite spirit) and because these thoughts and motions evidence a
degree of rationality (hence the spirit is another intelligent spirit). Thus, I infer the existence of other spirits, not from the resemblance of their
bodies to my own, such resemblance being totally unnecessary, but "from
their operations" - operations which, for Berkeley, reduce to alterations,
motions and combinations of ideas.
(Lorne Falkenstein, 'Berkeley's Argument for Other Minds', History of Philosophy Quarterly, Vol. 7, No. 4 (Oct., 1990), pp. 431-440: 431-3.)