So what does "soft" bipolar look like?

No mania. The "soft bipolar spectrum" includes bipolar conditions beyond classic mania; it includes depressions with hypomanic episodes (bp-ii proper) as well as those arising from cyclothymic and hyperthymic traits and those with familial bipolarity. The spectrum also includes hypomanic periods, which occur during pharmacotherapy or other somatic treatments.
Termonology? The term soft used to describe bipolar disorder is not one in common usage among psychiatrists. I imagine it could mean mild or could refer to something called bipolar ii disorder. Sometimes hypomania is generally less severe compared to what some may call: '"full blown" bipolar d/o. Generally, such adjectives are not particularly helpful as they aren't commonly agreed on by the medical community.
Depends. The term "soft" bipolar has been used by some psychiatrists to explain situations in which individuals who suffer from a mood disorder have episodes in which they experience some symptoms of mania or hypomania. For example, these individuals may have episodes of insomnia with high energy or racing thoughts. However the episodes may be very brief (1-2 days at most). This idea remains controversial.
Cyclothymia. Cyclothymia can be thought of as a low grade version of bipolar disorder. That is to say, cyclothymics do experience similar mood swings, but not to the intensity of those experienced by those suffering from bipolar disorder. A psychiatric evaluation is in order with appropriate mood stabilizing meds as needed and a referral to a reputable psychotherapist who specializes in mood disorders.