According to what I understand, early astrology recognized seven astral forces: Sun, Moon, Mars, Venus, Mercury, Jupiter, and Saturn. When people later discovered the planets Neptune and Uranus, how did this affect astrology and how they tied the astral forces to the visible planets?
Astrology is all about the perspective of the planets (which includes the Sun and Moon) as seen from Earth. It has always been considered that the more distant a planet, the less significant its influence. The outer planets become more subtle and affect longer periods of time.
This subtlety meant that earlier astrological pronouncements using only the visible planets were not negated by the discoveries.
When Uranus was discovered in 1781 it was seen to have a more elliptical orbit than the known planets and, of course, a longer orbital period. Astrologers sought to find a meaning for it and essentially extrapolated from the properties assigned to the known planets.
Uranus became the planet of unpredictability. Afflicted aspects to other planets were seen to disrupt the other planet's affect in unpredictable ways. This could perhaps, to modern eyes, be seen as bit of a cop out - we don't know what it does, let's make it unpredictable.
Uranus was then seen as the governor of old age. Its orbit of 84 years means that not many people see its Return (the Astrological return of a planet to the place it occupied at your birth).
In the natal chart, Uranus became known for discoveries, advancement, wisdom and progress. All these things were taking place at the time of the planet's discovery. The Industrial Revolution was taking place.
Neptune was discovered in 1846 and has an orbit of 165 years. Astrologers found it vague and assigned it power over vague areas. Neptune became the planet of introversion, addiction and mysticism. It was associated with artists - its strange properties influencing creativity.
Again, perhaps these were common thoughts in the psyche of the time. For both new planets they seemed to be associated with things that were happening in society at the time.
The effect of both these planets when in aspect with the better known planets was described according to normal astrological practice. Afflicted or beneficial aspects would be calculated to disrupt or enhance planetary influence just as, say, a Moon Square Mars would be seen to influence.
As a separate matter, Pluto is the planet of regeneration and renaissance. I haven't seen any astrological pronouncement on its astronomical demotion to dwarf planet.