Website Indexed and Ranked on Google

I am needing someone to assist in helping me get my website so it can show up on Google. I am not sure what I am doing wrong, but I have gotten backlinks recently, but my website still does not show up on Google or Bing and I am relying on direct searches for people to get to my website. I just want it to be searchable and ranked onto Google.
It doesn't have to shoot up to number one, I just want to get it started and for it to finally be there when you do a Google Search.