If you have a +10% attack speed on you weapon, you multiply in 1.10
If you have attack speed from any other items (not weapons), you sum up all the percentages, then multiply that in.
So, for example, if you had a 1.5 attacks per second weapon (all daggers) with +5% ASI, and two rings that each had +4% ASI, you would get:
1.5 * 1.05 * (1 + 0.04 + 0.04) = 1.701 attacks per second
That is the result that ends up on your stat page.
The speed you see displayed on the weapon itself in the tooltip includes the attack speed increase from bonuses on the weapon itself only, and not from other equipment. To compute your precise attack speed, you need to use the values based on the type of the weapon. For example, all daggers have 1.5 attacks per second, all swords have 1.4.
Note that if you're dual wielding, the number on your stat page will reflect only the weapon you will use for your next swing. To see the attack speed of the weapon in your other hand, swing once, and the numbers will switch to reflect your other weapon.