My camera lenses are getting particles and such on them, and whenever I take very close up (Macro) Picture, I can see these particles on the image. There are also fingerprints on the LCD screen. There is also other residue and such on my camera. I haven't cleaned it in years which would probably account for it.
Cleaning should not be done in an interval rather it should be a regular practice. I follow these regularly
That's mainly it.
This article will tell you what to do and what not to do: How To Properly Clean DSLR Camera Lenses
Here is a 'table of contents' with products you better don't use for cleaning your lens. You can find a explanation on the above mentioned website.
NEVER use the following products under any circumstance:
How to remove Dust Particles:
How to remove finger prints and oil based smudges:
How to remove water or rain drops
I agree with Hasin. Cleaning the camera and lenses should be done regularly. In some cases, after every shoot. That would depend on the environment and situation of the shoot, though. I recommend looking at Moose Peterson's video guide to how he cleans his gear.
In addition to cleaning the exterior surfaces of the camera and lenses, he talks about cleaning the sensor itself which is a necessary evil. Note, though, that this applies to a DSLR and not a compact camera. Even so there are many things he shows in the video that apply to cleaning a compact camera.
I don't think the particles you're seeing in your picture are coming from the lenses, though. Instead I am pretty positive that they are coming from dust/debris on the sensor itself. Contrary to popular belief, dust and scratches on lenses really do not show up in regular photography. See LensRental's blog post for a dramatic demonstration of that fact.