If you are using a form, you could try setting the forms properties to allow additions but not deletions or edits. Look at the Allow Edits, Allow Deletions, Allow Additions properties. If you are not using a form, not sure how you can do this.
There are several "Allow XXXXX" properties there that you should find helpful to disable on your form. You can also open a normal form in a manner that only allows it to be read, not modified; check the OpenForm Action (for a Macro) or Method (for VBA) in Access Help for how to do so.