I've faced this problem many times with family and friends concerned about their older macs.
This tutorial will show you how to easily speed up your system without the need of expensive software.
Let's get to it
Step 1: Disk Utility - Part 1
1) To open us disk utility go to Applications > Utilities > Disk Utility
2) On the left hand side of the Disk Utility window, you will notice your Hard Drive often labeled at the size, in this case 500gb, below it you will see the partition we need to fix, called Macintosh HD or something like that. Select it.
3) Towards the bottom of the central window you will see a button that says "Repair Disk Permission", click this and allow the program to do its thing. It'll may take about 30 minutes, so go grab a cuppa.
4) After that, you're done!
Step 2: Disk Utility - Part 2
2) Click that and again, let it do its thing. This may take a few minutes.
3) After that, look below the button, if the repair disk button is visible, click it and let it do its thing. If not, you're done! Be proud that you've just completed the first stage of computer maintenance! :D
Step 3: Startup Items
1) Go to System Preferences. (Taskbar or look in your applications folder)
2) Select 'Users and Groups'
3) Then Select your username from the list on the left hand side
4) Move your cursor right and look for the tab that says 'Login Items'
5) You will see a list of applications that load at startup, remove all of these programs by selecting it and clicking the " - " symbol towards the bottom.
6) You may be asked to input an admin password, input this at the prompt
7) Remove all the unnecessary programs and then restart your computer
8) Done! :D
If you're still facing speed issues move on to the next step
Step 4: Take Out the Trash
Be sure to clean out the Trash after sending the unnecessary rubbish to it.
This simple step may prove more useful than you'd think
Step 5: Hardware Updates
I won't go into the hardware side of things in this tutorial but if you're interested in researching further, I suggest you research increasing the size of RAM in your computer. This is simply the memory of the computer that allows it to compute data quickly. More ram, more speed... In theory (Starts at as little as ($30AUD)
Another thing you may consider is installing a Solid State Drive (SSD) these are a form of storage for your computer and lead to unbelievable speeds (Start at $70AUD) These are more costly than ram, but may be a useful upgrade sometime in the future.
I hope you found this tutorial useful and interesting. Hopefully you learnt something new from it.
If you did like it, I would really appreciate a rating or if you're interested in Mac Hardware and Software tutorials, follow me.