If you don't have a lot of feedback and not many items in your portfolio, you can work on personal projects or find people in your entourage who might need something, and show them as samples.
If there are skill tests that you can do, try to do a few to show your skills.
Buyers on these websites are aware that if you're just starting, it's normal you won't have many feedback; they won't always judge you on this only. At least you got good feedback.
Make sure you make it clear that you offer a constant communication, the revisions you offer, how many drafts, etc. If you're too general, they might not have time to personally ask you how you proceed.
For the same reason, your profile should contain your terms and your work process, guarantee, etc.
If you can get credentials somehow, it can help. Sometimes you need to pay to get them approved but they don't need to be from previous clients on that freelance site.
If you can get your identity verified, that's another good thing to do and it usually takes 20 seconds!
You can offer wholesale prices, free revisions (but be careful with that one!), urgent 24-48hr service, 1-2-3 months of free maintenance if you work on Wordpress websites, etc.
If you don't mind it, offer Skype or phone meetings. Some clients prefer to tell their instructions this way and have hard time explaining what they want, or simply prefer that "human touch". Make sure you note down their instructions.
Try to personalize your profile to not look too much like a lifeless robot.
Use good keywords if there is a section for it on the freelance site you're on.
Respond quickly to any communication and have some initiative when possible.
Observe the profiles and the way the "winners" approach the buyers and try to see what they do right.
Sometimes, if your prices are too low, buyers will think you do not offer a high quality service. Be observant of what they need and if you still want to bid low, make sure to explain that you do it because you need to build a reputation and that the price are temporary