The way to do this is as follows - and you have several methods that can help
1) Polygon Select - this works in Plan or 3D view or in Cutting Plane view. You can put a polygon (draw it using Polygon select tool) around a set of points that you don't want and then you can Create Region eg Junk and then add the points selected to that Junk region. Turn off the Junk Point Cloud region so once you have moved the bad points to that region they disappear off screen. This is not deleting the data it is just moving it to a region that you can turn off and not use in surfaces etc. Polygon select works in the different views. In 3D View - when you start selecting it freezes the plane of the 3D view while you draw the polygon (so you cannot rotate the view while drawing the polygon), but you can pan and zoom etc while selecting. One thing that you always find when doing this is that there will often be data in the background or foreground that is getting in the way that you don't want to select. You can use Limit Box to limit what is visible on screen while you are doing Polygon select - that way if you e.g. have a Tall Drill Machine in front of a Rock face that you want to keep while removing the drilling machine from the point cloud, you can use the limit box to hide the Rock face data so that it cannot be selected etc..
2) Cutting Plane and Plane Definition Manager - this allows you to define a Plane (e.g. a Vertical, horizontal, inclined or other orientation Plane) and then select that plane in the Cutting Plane View. The Cutting Plane View allows you to define a "Thickness" e.g. 4' (which would be 2' either side of the cutting plane). The Point Cloud is then sliced and only data that falls within the Cutting Plane and the defined thickness is visible. In that view you can also use Polygon Select to remove data that is "noise" that you dont need. The Cutting Plane View also allows you to step forwards or backwards by applying an offset eg 10' to see another plane and you can then select from that view. Each time you select keep Adding Data to the Junk Region - that way it takes it out of the Main Region and hides it.
These are the tools that I use and are part of the Surface Tools package in BC-HCE. The other tools like Extract Ground or Classify Regions are more automated ways to remove Noise / split Point Clouds into Trees, Buildings, Poles, Cables etc. but you need the scanning module to run those commands.
The basic Polygon Select etc tools listed above are all in the point Could Menus Ribbon and do a great job of removing Noise by manual methods and you can typically clean up a job pretty fast using them.
Hope this helps
Alan