Getting into orbit and flinging yourself into space are two different things, but achieved in similar ways. You go straight up for a while, then you go up at an angle for a while longer. Once you break about 40km, you've made it.
You'll need to keep your green circle (actually direction of travel) out of the red area.
All you have to do to fly is throw yourself at the ground and miss.
Yeah, getting that sideways velocity is the key, if you just go straight up, you'll just come back down again (or not if you're moving faster than the escape velocity), you need to get enough velocity along the ground so that you're moving fast enough that when you fall, you're going fast enough to the side that you miss hitting the planet. If you want a nice circular orbit, I just cut my engines and drifted up until my vertical velocity was about zero, and then aimed horizontal and blasted my way up to orbital speeds.
This is also really helpful:
https://gist.github.com/1073201 It's a table of the velocity you need for a circular orbit, or escape velocity, at a certain distance above the planet.
Edit: Ah, nice, there's a calculator.
My favorite design so far is a three stage system. The top stage (the one connected to my command module) is just 3 fuel tanks and a liquid fuel engine. Below that is a tri-coupler with 2 fuel tanks each and a liquid engine. Below that is 3 more SRBs. 3 more SRBs are attached to the liquid fuel cans.
All 6 SRBs are in the first stage, and their burn gets me up high enough to lean over. When it comes time to run your liquid fuel motors, run them at 75% or 80%. You should have no problem flinging yourself into space.
Yeah, I used something similar in my orbital rocket, although I had one less fuel tank on the top, and I had 9 SRBs attached around the bottom 3 liquid engines. And I had the stages set up, so all the SRBs and the bottom liquid rockets were all firing on takeoff, and then I could just jettison the SRBs when they ran out of fuel.
I got into a nice orbit between 275-325km. And I even had 2/3 of a tank a fuel left over, which was enough to de-orbit and land back on the surface. (where I inexplicably exploded on contact with my parachute open, while trying to land in the middle of an ocean.
18 minutes into an attempted orbit- 2000m/s and falling at 600k meters and rising. I sure hope this rocket comes back.
Check the chart linked in this post, at 600km, escape velocity is 2425m/s So you should end up coming back eventually.