The main difference is that the orbital speed is much higher in realistic: 7900 m/s instead of 1660 m/s in normal mode. You have a bonus on Isp, engines and tanks mass, but it's still more difficult.
In normal mode, on an optimized launcher, the payload will represent around 25% of the total launcher's mass. In realistic it will be closer to 5%. So if you want to send 5 tons in LEO, you will need approximately a launcher weighing 100 tons.
For the rest it's similar, but make sure you start building your horizontal velocity as soon as possible, don't wait to exit the atmosphere for that. Actually the atmospheric density becomes quickly very low, in practice when I'm close to reaching the orbital speed I'm still in the high atmosphere. Don't worry too much about drag, your biggest opponent is still gravity.