Entering through Entebbe airport

From the USA, you can pay USD$50 to get a visa from the Ugandan embassy in Washington DC which requires that you mail your passport.

Since July 1st 2016, you have to apply online in advance for a visa. Single entry Uganda tourist visa is $50 (at one point it was $100). 

The East Africa Tourist Visa costs $100.00 and allows entry into Uganda, Kenya or Rwanda. Again, apply online. This also applies to getting any visas for Kenya and Rwanda.

Specify how long you'd like to stay. Ask for as long as possible. max given at airport is 3 months but sometimes they only give you 2 weeks.

Entering overland

From Kenya - stock up with fuel in Kenya as it is more expensive in Uganda. The Malaba border crossing is the main one and is consequently the busiest and attracts the most hassle. The Busia crossing is not far away and somewhat quieter. Avoid the crossing to the north of Mount Elgon (on the way to Sipi Falls) in the wet season as the road can be atrocious. 

You don't need the help of a 'clearance agent' or helper to get through, it's all reasonably straightforward. Apply for all visas online in advance.

At customs, if you are bringing a vehicle in you have to pay 36,500 Ugandan Shillings (about $22) for road tax for 14 days. (This has increased). You can only pay in shillings so you will have to use the moneychangers, unfortunately. There was a 2,000 shilling 'bank fee' on top of this which is probably a scam but probably not worth arguing about.  If you have a 'Yellow Card' insurance certificate you won't need to buy car insurance at the border. Don't try and cross with a vehicle without a Carnet, it will cost you hundreds of $ in fees and bribes.