I have a group named "Group 1" which I want to have read permissions to "List 1" and have contribute permissions to "List 2".
How do I accomplish this?
Break the permissions on each list and then reassign the permissions on each list for that group
There's a thousand ways to skin a SharePoint site structure but I think the best is by permissions. When you create your structure, group sites, libraries, and lists together, based on permissions. You do this to avoid running into the administrative nightmare of updating permissions in 355435634 different places.
The easy way out (that'll cost you in the long run):
Simply, you could choose to remove the security inheritance from the list (List Settings > Permissions for this list > Stop inheriting permissions) and then add the groups you'd like. However, if those groups change then you'll have to remember every list you did this to.
The Alternative (for the love of all things SharePoint):
Set up your sites so that the lists "Group 1" need to edit are in a "Group 1" site, with that group being "Editors" of the site. You'll find this much easier to manage in the future, it also makes navigation easier for your users when everything of theirs is in one place.
Beauty of SharePoint is that you can assign different permission to Item Level
Break inherit permission for both list and than assign permission to both list manually.
To break inheritance for a list or library and restrict access to it, follow these steps.
1) Navigate to the site that contains the list and open it.
2) Choose the List tab to open the list ribbon.
3) Click Settings, and then choose List Settings.
4) On the Settings page, under Permissions and Management, click Permissions for this list to open the permissions page for the list. The permission page displays a status bar across the top that indicates the list inherits permissions from its parent site, and then gives the name of the parent.
5) To break permissions inheritance from the parent, click Stop Inheriting Permissions. This disconnects the list from the parent site.
Now assign read Permission to Group1 in List1 and contribute permission in List2.
The answer is very simple . just go to List 1 >list setting >permissions for this list> grant permission > Enter the group name "Group 1" ,select permission level "read" N.B: you have to break inheritance before doing all this.
Repeat this steps for list 2 and give "contribute" permission