I have a Cannodale 2010 Cadd 8
I would like to upgrade my cassette or crank gears to allow me to have another option for steep hills. At the moment I have a dual sprocket crank set and 8 gear cassette.
What would I have to replace to achieve the results I want? What makes are compatible with my bike and preferably the least costly.

The least expensive option might be a wider range cassette and/or a smaller inner chainring. That will probably call for a new chain, and may also require a new derailleur with more take-up capacity (longer cage).

Beyond that you can switch to a triple crankset, which will probably entail a new front derailleur (even if you don't change the cassette you'll also need a rear derailleur).

Step one is to use a gear chart like this one which will give you an idea of what sprockets and chainrings you'll need to get the gearing you want.

IMO- if it comes down to staying 2x8 with a cassette larger than 28 or 30 teeth, or going triple with a smaller cassette, say a 26t I'd spend the extra dough for the extra utility it'll give you. If you go with a very wide 8s cassette, you'll lose some of the middle gears where you do most of your riding. Going with a triple, lets you keep a cassette with more mid-range gears, while having the granny to give you the low range you want.

Being you have a double crank set best option is a cassette that has a wider range you can most likely go up to a 28 on the rear, but that also depends on the rear derailleur model but I'd bet you would be safe to 28 given you have a double up front.
That said going to a triple up front would mean getting a shifter for a triple the front derailleur may work but may rub in some gear combos easer, so replacing it may be needed so the over all cost is much more.
If you fill the need for something larger than a 28 in the rear a long cage rear derailleur will be needed you can get by by adding some links to the chain you have or just replace the entire chain.

Geostef, It'd help if you let us know what the number of teeth on the chainrings and the largest and smallest on the rear.

Brad

All rear derailleurs have a maximum cog and maximum chain capacity...

A modern long cage mtb derailleur can handle 34 teeth (cogs) and probably has a maximum capacity of 36 - 38 teeth.

Calculating the maximum capacity is done by subtracting the number of teeth on the smallest chain ring from the biggest and adding this to the difference between the largest and smallest cog.

If your chain ring and cassette numbers do not exceed the maximum capacity you should be fine and swapping the road rear d for an mtb long cage and a wider range cassette should not cost much and let you retain the double crank and your existing shifters.

https://sheldonbrown.com/gears/

This is important. We need to know what you're starting with to suggest the best modification. For example, say you have a 53/39 crank and 11-23 cassette. In that case I'd suggest a cassette with a 28T low gear. See how you like that. If that's not enough, there are more options after that.

The Cannondale catalog says the 2010 CAAD8 8 came with compact crankset (50/34) and a 12-26. You must have a CAAD8 8 because thats the only 8-speed version.

Going from goatalope's specs the current chain capacity on the CAAD is 50-34 + 26-12 = 30 so with a long cage rear d a cog with a range as wide as 12-32 could be used with the current chain rings and not exceed the derailleur cog limit or capacity.

That would give a nearly 1:1 low gear or 28 gear inches which should handle some exceptionally steep grades and be good for everything except loaded touring where the lows are usually lower.