Here's a few rules of thumb if you want the effect known as BOKEH (Boh-Keh) Its Japanese for Fuzzy. Americans say it Bow-Kee - but Its a Japanese word, you dont see Chinese ppl like me saying America like Am-er-ay-ka)
Anyway. Here are some steps to focus on for the time being to make the background as blured as possible.
1) get closer to your subject
2) the background needs to be as far away as possible.
3) Set to Av mode (or A mode - or Apeture Priority)
3) If shooting at f1.8, make sure the subject is completely in focus. Sometimes the persons nose and face is focused but the ears and hair is all blurry. If this happens, start shooting at f2.0 or 2.8
4) Keep your ISO as low as you can possible allow
5) If you can or have the ability, use the longest focal length possible, combined with the LOWEST apeture number you can get.
6) If the background isnt making it happen then change the background
7) if you want the background to have little Bokeh balls (balls of out of focused light) Find a background with small, distant and strong light sources. Eg, the sky poking through the gaps of leaves of a tree. (Like the first photo you posted)
Keep shooting, and good luck.
1) Olympus OM1 [Zuiko Auto-S 50mm f/1.8]
2) Pentax MZ-60 [Sigma 28-90 & 100-300]
3) Canon 7D [EF-S 15-85 & 70-200mm f/4 IS & 50mm f1.4]
4) Leica M [50mm Summicron Pre-aspherical - Silver]http://www.poetproductions.net