inland makes good points.
Look around on Fishpal and get an idea of which rivers and beats you may want to fish then start contacting those estates as soon as you have your dates. While rods can become available at a moments notice, often for discounted prices, you cant rely on things being available the day before you want to fish or even a week or two before you want to fish. Its an unfortunate reality that you must pay up front and if conditions are crappy, you want to switch rivers, etc. then you are out that money and you must pay again to fish somewhere else.
Also, some of the estates will let the river, or their section of it, for a set fee per week (6 days fishing) per number of rods as inland has mentioned. Meaning, the fee might be £1500/week for 4 rods which, when split 4 ways @ £375/rod, seems 'reasonable' (at least, reasonable in terms of whats the norm for atlantic salmon fishing, especially in Scotland) you cant simply book 1 rod and expect to pay your share -- you book them all or none at all, and thats if the week is even available.
In addition to Fishpal, you can also check the Sporting Lets site:
Salmon Fishing in Scotland | Trout Fishing Scotland | Loch and River Fishing, Scotland
These lets are typically going to be as described above, you must purchase the entire week, all rods, or not at all, but its something to look at and you may contact them and one of their agents will try to get you sorted (aka try to get you to spend your money on one of their fishing lets).
Anyway, the prices double come May once the fish start coming in and keep on going up through the year, and July and August are grilse time, but many of the rivers, especially the small Highland rivers, are really neat. Ill send you a PM with suggestions on 'cheaper' fishing Ive done in the past there.