What can I do to speed my computer up?  

What is the specifications of your laptop PC?

My first suggestion would be to turn off those startup programs that you don't need during boot up..

After that, it would be advisable to defrag your laptop's hard disk...

Last but not least, see if you can upgrade the memory - if you are using 512MB memory, upgrade it to 1GB...

Delete the stuff on your computer that you don't use. Like documents and programs.

Does the computer run slow all the time or just when you are on the internet?

If it runs slow all the time you need to buy more RAM for it. If it runs slow just when you are on the internet it is because you have DSL. Nothing can be done to help you unless you switch to a cable modem.

I have just bought my computer last January, and because I want my computers to be equipped with softwares I would really needed, I keep on downloading softwares, and my sisters are fun of music they also asked me to download videos and mp3 on my pc. Aside from that my computer becomes stuck with many pictures.

After a week, I notice my computer runs slow, it really annoyed me, so what I did is I erased softwares that are less used, erased some of those music videos and mp3s and erased the pictures after having it attached to my email. Then my computer runs faster again.

A few days after I started joining on many paid to post sites and paid to participate survey. My computer gets slow again so what I did I follow the response of a friend of mine in other forum. He said I should have my cookies clear every now and then and I should always regularly anti-spyware software to remove spyware that may have been in your computer. Those spyware will cause to slower the connection. And through he is of what he said. After I do his advise, my computer runs faster again. So now I always do those things above whenever I my computer runs very slow.