Speed of Voyager 1

Rocket fuels initially, followed by a series of gravitational assists (slingshots): http://en.wikipedia.org/wiki/Gravity_assist The linked article mentions Voyager 1 mission as an example.

Gravitational force decreases with distance squared. So the deceleration due to the sun is negligible at that distance.

Acceleration due to gravity is given by $\frac{GM}{r^2}$, where $G$ is the gravitational constant $6.67\times 10^{-11} \mathrm{m}^3 \mathrm{kg}^{-1} \mathrm{s}^{-2}$. The mass of sun is $2\times 10^{30} \mathrm{kg}$ and the distance is $2\times 10^{13} \mathrm{m}$.

Plugging those values in gives a slowing down of $3 \times10^{-7} \mathrm{m} \mathrm{s}^{-2}$, or losing $300$ nanometers per second every second.