Id first get out there and try shooting in aperture priority and then in manual and see what effects this has on the quality of your photos.
Do you know the relationship between Aperture, Shutter speed and ISO regards getting a correct exposure ?
Some times there just isnt enough light so a slower shutter speed is needed which will then probably need a tripod or some other support to stop camera shake.
A wider aperture (lower fstop) will let more light into the lens but a fast lens can cost a lot of money and using a wide aperture shortens your depth of field.
Increasing the ISO, I learnt to shoot on 35mm and medium format so increasing the ISO meant changing your film (unless you had an understanding lab tech and you "pushed" or "pulled" the film) but on digital its a lot easier but increasing the ISO can increase noise to the image.
All these work together (in reciprocity), adjust one and you have to adjust another to keep the same exposure.
The other thing we can do is add light, flash, street lights, car headlights etc but you just need to play and have ago without relying on the cameras auto mode.
One other thing, try shooting in RAW. This will allow you to "push" and "pull" the exposure like we used to do with film and lets you manipulate the image better than you can with jpg.
There was a hack for the 300D available some time ago to let it shoot RAW.
Also, one other other thing
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, go out and limit the number of shots you take, go for a walk and spent you time taking 20 well thought out well exposed shots rather than clicking away taking 200 hoping some will come out OK.