I'm using wp-2.71 Atahualpa 3.33

By default, recent post, links, and meta widgets are shown in the right sidebar, but when I put my own widgets in it the sidebar deletes the default widgets without releasing the use of the default widgets.
That is to say
Right Sidebar hogs meta widget and NextGEN slideshow widget after I put my own widgets in the right sidebar, so I can not use them. These two widgets are always unavailable.

Can anyone helps me out of this please. I'm a newbie.

First off - what version of WP and Atahualpa

Wordpress installs a couple default widgets during the install - Categories and Archives on the left and Recent Posts, blogroll and Meta on the right.

Once you add a widget, you are telling wordpress you want to control the sidebars, so it removes the default widgets. If you want them in, you must add them manually at this point.

I'm not clear about what is happening to the Nextgen widget, please give a detailed explaination.

I don't know how to put this even more clearly but meta widget and some other widgets are not available in Atahualpa3.333 (always), even I put my own widegets in right sidebar (stop using default widegets).

Since I can't recreate this, could you try a few things.
1) switch to another two column theme and see if the same problem exists there.
2) remove all the widgets from both sidebars, then
a) verify that only the default widgets are there
b) document, step by step what you are doing i.e.
1) go to appearances-> widget
2) select right sidebar and press 'show'
3) press 'add' on the meta widget etc,etc
this will give me a flow to follow incase I am skipping, or doing something extra, than ou are doing