Trailhead provides a really nice overview of Salesforce Custom and Standard Objects and how they are structured https://developer.salesforce.com/trailhead/force_com_introduction/data_modeling/objects_intro.

Setting up an Object

The minimum steps required to set up an Object. 

• Create the Object, name it
• Set the Name field on the object - eg Auto Number
• Set the details on the Object
  • Allow Reports
  • Allow Activities (optional)
  • Track Field History
  • Set Deployed
  • Allow Search
  • Create Tab
• Create the Tab for this Object
  • Decide who should access the Tab
  • Decide which App the Tab should be in - HINT! NOT ALL OF THEM!
• Optional - Create Record Types
• Add the Fields to the Object
  • Include Help Text
  • Set correct Permissions as you are creating the field
  • Include Lookup or MD fields to other objects. 
    • Remember to set the Lookup Filters if required.
• Edit the Page Layout to ensure that all the fields are visible and in the right location
  • Make the Section header visible for System Fields
  • Ensure required fields are required. 
  • Add Files and Notes related list (if you are using them). 
  • Add Object History related list
  • Override the Salesforce Mobile and Lightning Experience Actions
    • Set the exact Actions you want to appear on the Object
• Optional - Create other Page Layouts if required for other Record Types
• Optional - Create a Create Record Action from a related Object
  • Ensure the Layout is correct with all the required fields required for Creating the record
• Optional - Create an Update Record Action for this object so records can be bulk updated from the list view
• Create the Compact Layout and assign it to the Page Layout
• Set the Search Layouts - IMPORTANT! 
• If there are any buttons to add to the List View, then add them
• Optional - add any Validation Rules 
• Set permissions on Object
  • Optional - Set Record Types defaults
• Enable Feed Tracking for the Object
• Look at the Object, create a Test Record. 
• Edit the Lightning Page. See Lightning Record Pages
  • Chatter first
  • Delete Related
  • Add Related List Quick Links IF there are related lists. 
  • Add Files as a Related List under Chatter. 
  • Activate Page - Assign as Org Default.
• Go to the Tab
  • Edit the All View
  • If there are any Record Types, create a View for each Record Type
  • (Ensure you go back to Classic if this will be in Communities to ensure Communities users can't see Inappropriate Views). 

Fields

This video from Trailhead is a really good overview of creating fields https://www.youtube.com/watch?v=j95gONjVNFU#t=11

• The most annoying thing about fields is not seeing ALL fields in alpha order - so have a good idea of what are the custom and standard fields in your org. 
• Also see each object below for the standard fields that are not set as visible by default, which is kinda annoying (eg Contacts). 
• The most important thing about fields is the security https://help.salesforce.com/HTViewHelpDoc?id=admin_fls.htm

See Rules for Fields

Relationships

Trailhead has a good overview of Relationships https://developer.salesforce.com/trailhead/force_com_introduction/data_modeling/object_relationships

Remember, Master Detail relationships are great, but you can always use triggers, or Rollup Helper to create calculated fields if you don't have a Master Detail relationship. 

Standard Objects in more detail