Depending on who you're working with on the customer-side of the house, the general workflow for consulting and custom engagements is a statement of work that lays out the "what" and "how" of your future deliverables as well as reasonable expectations on both end. You can include timelines, milestones, price expectations, etc in the statement of work (SOW). Fundamentally, the SOW helps to set expectations and communicates what each party should expect. The vendor (you) should come up with you own template and format that you send to your enterprise customer for review and approval - there should be signoffs on both sides. It usually helps that a higher ranking executive with legal authority to enter into contracts review and sign the SOW.
In addition, the most important part is billing. Your enterprise customer might need a formal quote of total cost. Some enterprises want to see breakdowns but others are okay with just a few line items. The level of detail required is usually dependent on the total cost, internal financial controls, and culture. One thing to note is that it's common to have to work with a procurement specialist at larger enterprises. These specialists are there to save the company money and may beat-you-up on the price, so keep that in mind when you price out such an engagement. Also, the specialist may also force you through an RFP/RFQ process, which can be painstakingly long. Again, the specialist's job exists to save the company money so they may request/require competing quotes before the purchase goes through. The decision on whether a project "goes out for bids" often depends on the total cost as well as relationship between the budget owner and procurement.
Lastly, you'd invoice according to terms (net 45, 5/30 net 90, etc).
The cost is up to you to decide. The enterprise may ask questions to size you up. How many employees, DUNS number to obtain business credit ratings, etc. A larger enterprise may prefer to buy services from a more established organization as opposed to a small one based on a risk standpoint (what happens if the small company flops mid-project? or what about the long term viability of the company taking into account future support needs?). If anything, find out what your costs are and work in a 20-40% margin. When all's said and done, you'll likely have to settle for less (sometimes far less unless you walk away) than your initial quoted amount. The rare occasion where this doesn't happen is if the total cost is low and there's no direct competition (i.e. other vendors that can offer the exact same product AND the enterprise has a direct need for your services).