The two main ways of getting to Uppsala from Arlanda airport to Uppsala is by train or by bus 801. The train is more frequent and faster (the train takes ~20 minutes, the bus is ~40 minutes), while the bus is cheaper (the bus is 120SEK, so ~11 EUR or USD; the train is typically 197SEK).
The easiest way to purchase tickets is via an android/ios app. One can also buy a ticket directly on the bus by tapping a credit/debit card. Train tickets from Arlanda to Uppsala can be bought from a person at the entrance to the airport train station. Otherwise you can buy train tickets from a ticket machine or at 7-Eleven / Pressbyrån stores.
The bus company is UL, the train companies are SJ, SL and Mälardalstrafik. The SJ app can be used to purchase train tickets for all 3 companies; note that in the UL app you need to buy the "75 minute ticket to/from Arlanda by bus".
Link for train app for android
PS. If you take the bus to Arlanda, do not get off at "AR-terminalen": it may sound like "ARlanda", like the airport, but it's actually a random parking lot20km from the airport.
Walking
For a nice walk to Ångström, walk along Bäverns Gränd (street extending to your left as you leave the hotel) until you reach the bridge, then across the bridge, then immediately left to the park (Stadsträdgården), walk along the river till the next bridge, take a left there, up the hill (there are 2 different routes up - concrete is faster and boring, forest path is slower but nicer and you can find wild strawberries along the way), then head in the same direction (southwest) for another minute and you'll see the building on the horizon, it's smooth sailing from there.
Here's roughly what it looks like:
Bus
The only bus from the central station to Polacksbacken (bus stop closest to Ångströmlaboratoriet) is bus number 4 towards Gottsunda. Note: you board the bus through the front door, both if you tap a credit/debit card or if you purchased a ticket via app above.
The talks are in room 4101. Once you enter Ångströmlaboratoriet (e.g. from the bus stop), there will be signs pointing to it, but you can also see a map following this link:
An approximate description: walk past the reception, then past the statue of an ostrich(!), then one floor up, straight ahead for another 15 seconds or so, till you face a crossing (and Maxwell's equations!) - room 4101 is directly to the left.
Here's approximately what it looks like: