I am new to investing, and am looking for what is the best way to invest. Due to religious reasons I do not want to make money by interest. Are there any other ways to get a decent amount of earnings short term without interest. Also I am not looking to be making thousands every week, but just a few extra bucks at the end of every month/week.
There are several market indices put out by Dow Jones that track companies that are compliant with Islamic investment rules.
You could either find a tracker fund that tracks one of those indices (and is, itself, compliant), or invest directly in the companies that comprise the index.
The type of investing you seem to be targeting is often called "Income investing". The goal with income investing is generally to maintain the invested principal while having some cash flow generated and disbursed from the invested principal. I am ignoring a discussion of the 4% rule generally associated with retirement income investing.
Most income investing focuses on three sources of return: interest, dividends, or payment for asset use. The first two are probably obvious, the last is where you own an asset and someone else pays you for the use of it. A common example would be renting out real estate.
Expecting a weekly flow is unlikely, you would most likely have to deal with quarterly payments and budget those for your weekly goals.
This might be a useful read: http://online.barrons.com/articles/SB50001424053111904223604579489760514346406