• Go with only the respected names.  It is fine to go with one of the consolidators for credit cards, for example, Credit-Land, Credit-Card-Analyzer, Credit-Card-Applications-Center, and many others or you can always visit the websites of CitiBank, Providian, American Express, etc.
• Take a look at the website to make sure that you are on the right website.  If in doubt, leave the website immediately and try another website that you can trust.  (Related:  How to prevent identity theft)
• Enter your information carefully and make sure that you have all information correctly filled out before you hit the "submit" button.  If there are confirmation pages, print them for your records in case you need.
• In most cases, the approval will be instantaneous, particularly with banks like Chase Credit Card and others.  If not you will receive a notification telling you when your application will be processed and the decision communicated to you.
• Most websites require you to submit the application in one session but others also offer the option to create an account and save whatever information you have submitted.  You can go back later to complete it.  While more convenient, I would still say that you should get all the information regarding your social security number, annual household income, address, phone number, mother's maiden name, etc. in one place and then just complicate the application.  (Related: Online shopping safety)

What to watch out for if you have bad credit?

• Just because the application can be submitted online with no customer service person harassing you, it does not mean that you should submit 25 applications.  It is a good idea to research as many banks as you can and then develop a short list of which ones meet your criteria, you should only apply to one.  Every time your credit is checked, a record is made.  If you get instant rejection, then apply to the next bank.  It is less damaging to your credit if you apply to several banks within a small window of time.
• If you get approved but do not like the terms and conditions, you should not accept it.  A bad card will actually hurt you in the long run.  If possible, cancel it even before it is delivered or you should not activate the card when you receive it.
• Use your newly acquired credit card responsibly (How to stop overspending).  Think of it as an opportunity to repair your credit so that you can enjoy the many benefits that people with good credit enjoy (e.g. lower interest rates).

Related links:  Debt consolidation tips       Banking services for college students