I have installed SDL Tridion UI 2012, now Iam trying to edit the page component text in my staging site the problem is that after doing the edit and clicking on the Finish Editing button the page refreshes but my changes don't get visible, now if I click the same component in edit mode my changes becomes visible. The strange behaviour happens when I closed the application and start it again now my changes starts appearing even if I am not editing the component, which I believe should be the actual behaviour. My question why the recent changes not get visible after clicking the Finish Editing button. Why I need to close the browser and start the application again. What I have missed in my installation steps? Please help.
That's exactly what Session Preview should take care of - after you click "Finish Editing", the page should be refreshed and show your changes.
If you're not seeing this, then it looks like Session Preview is either disabled or not configured correctly.
Seeing the latest when editing...
When editing, regardless of Session Preview's setting, you should see your latest (minor) edits as they exist in the Content Manager. You can double check by comparing the same component in the CME. After editing and when you click off of a component your edits are saved (as a minor version).
Old content showing...
I've seen old content showing when authors click off of edited content usually when Session Preview is partially set up. When content is outdated the Update Preview button will flash to let you know to display the latest updates (even when Session Preview is mis-configured).
Clicking on it should show you all of your minor (and others' major) updates. A green border and pencil icon will also hint that there are pending changes. Without Session Preview on or working, then you must publish to see all of your page changes on Staging (default behavior in SDL SiteEdit 2009).
Restarting after Finish Editing... (works because of a publish to Staging)
If you're seeing changes when not editing but sometime after "Finishing," it might mean Finish Editing published your changes to Staging successfully (it should). Look for a notice to refresh the page. You don't need to restart your browser though, a refresh should do the same.
Most of the time I have seen this happening when CD is not able to properly map the publication, ensure in your staging site cd_dynamic_conf.xml the proper publication mapping is done, also in the cd_storage_conf.xml session wrappers configured properly and cd_ambient_conf.xml has the session preview cartridge. Also make sure your staging site has a ambient data and preview modules configured.