I have been a member of several groups, as well as sole ownership.
First thing is to be happy with the other members of the group - it is not always about the money. Nothing is more irritating than one member not cleaning the aircraft, fuelling it, or generally not "pulling their weight" etc.
Money is of course important, I have never been a member of a non-equity group (how can it be group ownership without equity??).
Basic principle is that all members have an equal share in the assets of the group (aircraft, cash at bank, spares etc) which they have paid for.
Each member pays a monthly fee whether they fly or not - to cover the "fixed overheads" - insurance, hangarage, permit/CoA renewals, etc
In addition each member pays for hours flown (wet or dry depending on agreement) to cover maintenance costs, oil, etc
The monthly and hourly costs should allow the build up of a reasonable fund over a period, for major costs such as overhauls, repaints, fabric re-covering etc.
If there is an unexpected requirement for funds (e.g. blown engine) and there is not enough in the pot then a call may be required on all members to cover the cost, so be aware of this and make sure you have access to some funds if needed.
The big advantages are much reduced cost over sole ownership and (with a reasonably small group) access to aircraft whenever you want it.
Going back to my opening point - the other members are the key to a successful group. Do you all get on? Do you all have similar aims? Do you all have sufficient income? Is the agreement fair and equal for all members?
I have never regretted using group flying but would never join a group where I did not know the other members reasonably well first.