Looking over the comments, the video by GoSlash27 may be too ambitions (trying to launch directly into docking with the target) for beginners.
Here is how I do it....
As to your problem (which is getting close) I agree there are some good videos out there. But I'll run through it once...
Part one, getting kinda close....
1) Get into an orbit that is similar, but not identical to the target.
a) You want the orbits to touch at one point (or one crosses the other a bit).
Usually, for low Kerbal rendezvous, I set the periapsis of the ship to touch the orbit of the target and the apoapsis to be maybe 100 km higher than the target orbit.
c) The orbit have to line up (have the same inclination). In the map, click on the target and choose "select as target". Then you will see "AN" (ascending node) and "DN" (descending node) labeled on your orbit with a number (the number of degrees by which the planes of the orbits don't match).
d) These points are the places where your obit plane crosses the plane of the target orbit. At one of these you have to burn to make them match. Burn straight north (if the number is negative) or straight south (if the number is positive) until the number is zero. (Closer to zero you get, the easier the next steps will be).
e) At, or near, the point where the orbits touch, you will see the indicator(s) of closest approach. (If you can't see them, the orbits don't line up or they don't cross").
f) You will also see where the target will be when you reach the closest approach (and hovering over the closes approach indicator will show how far you will be from the target you will be at closes approach). (the intercept.)
e) If you put a maneuver node just past the closest approach, it will show you the next closest approach after the maneuver node (ie on the next orbit).
f) Your keep clicking on the maneuver node to set it ahead one orbit, you will see the next closest approach on the next orbit(s).
g) As you do this, you will see the indicator of where the target is move showing its position on the different closest approaches.
h) Do this until you get a close approach.
i) then use the node to adjust that approach (burning prograde or retrograde) until it is as close you are can get it. (A few km's or less, hopefully).
j) make sure you don't adjust the orbit so you hit the atmosphere or ground, if that happens, try the orbit before or after instead.
k) For me, with an orbit bigger than the target one, I usually can see the position at closest approach get closer and closer as I advance orbit by orbit. I do this until it passes the intercept. Then burning retrograde moves it back to match up. This has the advantage that I'm bringing the orbits closer together (with will make final approach easier).
l) Once done, you wait until you reach this closes appoach and then match speeds.
Step two, getting close.
a) When you are within 25-50km of the target, use your nave ball (set on "target" rather than "orbit") to turn your ship so that if points away from the relative direction of motion (the yellow circle with three lines sticking out and a cross inside). This is the direction that you will need to be pointing to kill the relative velocities (and match orbits).
as you get close to the intercept setup above, switch out of map mode. When you are within 25-50km of the target, you should be able to see the target indicated on your screen with the distance listed.
c) You intercept indicators will be telling you how close you can expect to get.
d) At that point, the target will be off to the side moving laterally.
e) Just before this point (allowing time for a burn, you will have to play with this until you get a feel). Do a burn away from the direction of relative velocity (as above) until the relative speed (as indicated on the nave ball) is as close to zero as possible.
f) If you burn too much, flip around and burn again to get to zero.
g) Now point your ship toward the target.
h) Do a gentle burn to move slowing toward it.
i) If you have RCS thrusters, you can use them to try and line up the relative velocity indicator with the direction the target is in. (Making you move more directly right toward)
j) When you get as close as you are going to (or before you run into it), flip away from the relative velocity and do a burn as with "e & f" above. (Or use your RCS thruster to kill you relative velocity.)
k) You are now relatively motionless with respect to the target, but closer than you were with step e & f)
l) repeat steps g-k again until you close enough for the stranded Kerbal to EVA and fly to your ship.
