You've found the Spanish property that you want to purchase. Either you'll have signed a private agreement, or you'll proceed directly to completion.
One of the peculiarities of a completion of a real estate transaction in Spain is that every completion is attended by all of the parties - the buyer, the seller, the estate agent or estate agents, the lawyers, the bank or banks, and the Notary, all meet at the Notary's office. The content of documentation may have been agreed in principle prior to the meeting, or perhaps nothing will have been prepared until the parties arrive for the meeting. There may have been a lot of waiting around and negotiations, and finally the Notary will read through the documentation to be signed in Spanish. And either the Notary or an appointed translator will translate whatever the Notary says into English, or German, or whichever language any of the parties speak, if they don't understand Spanish. Finally the buyer, the seller, or their respective representatives and the Notary will sign the document, and the buyer will hand to the seller a bankers draft or a number of bankers drafts amounting to the purchase price. It's possible that one or more of the cheques will be made payable to cash so that the seller can hand them to the estate agent or anyone else who expects to receive payment once a transaction is complete. Each of the cheques will be photocopied and a copy will appear in the completion documentation. In my experience, the vast majority of transactions that head towards completion proceed to completion. That said, it's rare that any transaction will complete without a fair degree of complication.
For example, the property may be security for a loan so that either the bank will either have to provide a completion certificate so that you can retain sufficient funds to pay off the bank after completion, or one of the bank's representatives will attend the completion meeting. The buyer and seller may want to complete quickly and the bank may not have a representative immediately available.
Another example, the area of a plot of land may appear smaller on the property register than it does on another register, the catastro, a register maintained by the Spanish tax authorities. Steps may need to be taken to rectify the property register to reflect reality. Although that's an issue that ought to be ironed out before anyone arrives at the Notary's office to complete the transaction, it's often the case that those sorts of issues are only considered at the last minute.
Once all documentation has been signed, the purchaser has made payment to the seller, the Notary's staff will prepare a document that will be used as evidence of the transaction, in order to pay purchase tax and register the property in the name of the purchaser. That's a document that you'll get to know as being the Escritura, the document that you will put in your file as evidence of your purchase of property.