As soon as you turn your laptop on, start the Task Manager. (Right-click on the task bar at the bottom of your screen or press Ctrl-Alt-Delete). Click on the 'Processes' tab. Maximise the window, so that it fills the screen, and then minimise it down to the task bar.
The reason for doing that is that I'd like you to examine what the Task Manager shows when everything is going slow but it can be almost impossible to open the Task Manager once problems are already occurring.
Try to use the internet as normal. If everything seems to be grinding to a halt, click on the Task Manager button that's now on your task bar. Look down the 'CPU' column for any high figures. You can ignore 'System Idle Process', which should be showing a figure in the 90s, but anything else in double figures should be noted as it's almost certainly the cause of your problem. (If you don't know what to do about it, post again to tell us the name of the process).
If the only high figure in the 'CPU' column is for 'System Idle Process', look down the 'Mem Usage' column. You're looking for anything with EITHER a very high figure OR a figure which is constantly changing (even if the actual figure is quite low). Either of those symptoms could indicate a possible problem. (In particular, if you've got Microsoft Security Essentials installed, check that MsMpEng.exe doesn't have a high or frequently changing figure next to it). If anything looks unusual, please tell us what it is.
Please tell us as well which browser you're using and whether you've got any add-ons (such as tool bars video downloaders or ad blockers) installed with it. Further, please tell us whether you've tried using a different browser (and what the results was).
AS O_G suggests, it's well worth scanning for malware (which has a nasty habit of slowing computers down). Download, install and run the free version of Malwarebyte's Anti-Malware from here:
http://www.malwarebytes.org/products/malwarebytes_free/
(NB: When installing it, click to remove the tick which offers you a trial of the 'PRO' version).