I went through an angel round and a Series A myself. I will focus on a first time entrepreneur's case and use realistic numbers.
1) You have and idea. You make as much progress as you can before trying to raise.
2) Ideally, you network with some angel investors / micro VC's before you start talking about your round.
3) You incorporate your company. You will issue an arbitrary number of shares for the co-founders (typically 10M+) and you allocate some shares as an option pool (typically 10-20%). Option pool will be used to give shares to employees, advisors, consultants and board members.
4) You decide that you have made enough progress to raise a round (doing this too early will be bad for you)
5) You talk to a lot of angel investors and early stage VC funds. Angel investor is somebody who invests his/her own money, VC is a person who invests other people's money. That's the only real difference.
6) If somebody is interested, you start talking about the terms. Now you really have to learn the jargon.
Let's assume you will do a traditional priced round. You will negotiate a pre-money valuation (typically $2-10M for first time entrepreneurs). Let's say an investor proposes you $1M with a $4M pre money valuation (means your post-money valuation is $5M) and you had initially issued 10M total shares. Each of your shares will be worth $4M/10M = $0.25. Your company will issue $1M/0.24 = 4M new shares for your investors. So you don't actually sell shares, you just issue new shares which will reduce your ownership percentage of the company(by 20% in this case). This deal could be done with a single investor (usually a VC) or a group of investors who are each putting smaller chunks.
There's another format called "Convertible Note/Debt". It has become popular in silicon valley. Instead of negotiating a pre-money valuation, you negotiate for a discount rate (let's say 25%) and an annual interest rate (let's say 8%). In this case you don't immediately issue shares to investors. Instead you promise to give them shares when you do your next priced round (Series A) with the valuation that those investors pay / (1+discount rate) / (1+interest rate). For example if you get a pre-money valuation of $20M a year after the convertible note, your angel investors will get shares worth $1M(1+0.25)(1+0.08) = $1.35M from the $20M pre-money valuation. That will be $1.35 / ($20M / 10M) = 675K shares.
The most common format these days is a convertible note with a cap on the valuation. Typically the cap is negotiated just like a valuation. If you get a valuation higher than the cap in your Series A, angel investors will get shares from the cap you agreed on instead of the full price.
7) Typically, the investors give you a term sheet. When the negotiations are over, they go through a due diligence period. They will ask for some docs to check there was any BS in your pitch. In a seed round, this is usually very lightweight.