One thing to keep in mind is that SSRS report access is Windows Authentication only. This means that the users accessing the URL must have permissions on the server to get to those reports. One thing that really messed me up at the beginning, I could see the reports, but the users that were testing it couldn't get to it. Reason: All users must have access to the main landing page in SSRS. I, as local admin, had access to it, but they didn't since they weren't local admins. Make sure all users using the reports have access to the main page. Then, the best thing to do is to put the reports in individual folders (grouped by what they do, for instance), and set appropriate permissions for each of these folders, or even to the individual report. That way, everyone can get to the home page, but only if you have permissions to each folder can you click on it and have access to the reports in it.
Don't confuse this with "I am using a SQL username and password to get to my data". That is totally different. That is how the report actually gets to the data. The issue above is that the individual users that are going to be running the reports must have Windows access to those pages in SSRS to then get access to those reports. Keeping these two things in mind should help greatly.
One way to accomplish the Windows authentication to the reports and directories is to set up local groups on the SSRS server. Then add Domain users to each of the desired groups. Then give those groups access to the directories and/or individual reports. This makes it as easy as adding a user to a local box group to give someone new access to the reports they need. A normal sysadmin could do this, and wouldn't have to know how SSRS is set up.
It is explained in detail below. Hope all this helps.
How to use Local Groups to frame the SSRS permissions
If on Server 2003, do a right-click on My Computer and choose Manage. Under System Tools, expand Local Users and Groups.
On Server 2008, go to Server Manager, and expand Configuration on the left side, and expand Local Users and Groups.
Create a new local Group (right-click Groups and choose New Group), something like SalesReportUsers, and add Windows users to it that are ok to run the reports. You can also add another group called SalesReportMakers, and add Windows users to it that you will allow to actually create and install reports.
Also, create a group that will include ALL domain users, something like AllRptUsers.
Note that SSRS requires windows authentication for users who run or create reports (the actual reports can use Windows or SQL Server authentication for the data retrieval).
Then, in the SSRS administration screens, set the permissions for each directory and/or specific report for the local group that should have access to those reports, or creation permissions.
Important - Make sure to give the AllRptUsers local group access to the SSRS home page. That way, all users can see the directories, but only the ones that have access to those directories can actually choose them and see what is in them (once those permissions are set as well). If this is not done, nobody will be able to get to the SSRS website, since no one will have access to the home page.
Then, as new users need to be added, just figure out what groups they should belong to and add them in the Local Groups as Windows users. The SSRS permissions are already set for those groups (assuming you did so above), so no further action would be needed.