There are several excellent solving guides available on the internet so, rather than trying to explain these techniques, here are links to three of them.
nd's tipsRuud's solving guideSudopediaTwo of the most important techniques are the 45 rule and combination analysis. It is very useful to have access to a combination calculator. The one I use regularly is
Ruud's combination calculator which is very useful because one can specify required and forbidden numbers which reduces the number of possible combinations.
I've also compiled my own Cage Combinations table, which is listed below.
2-cell cages3(2) = {12}
4(2) = {13}
5(2) = {14/23}
6(2) = {15/24}
7(2) = {16/25/34}, no 7,8,9
8(2) = {17/26/35}, no 4,8,9
9(2) = {18/27/36/45}, no 9
10(2) = {19/28/37/46}, no 5
11(2) = {29/38/47/56}, no 1
12(2) = {39/48/57}, no 1,2,6
13(2) = {49/58/67}, no 1,2,3
14(2) = {59/68}
15(2) = {69/78}
16(2) = {79}
17(2) = {89}
3-cell cages6(3) = {123}
7(3) = {124}
8(3) = {125/134}
9(3) = {126/135/234}, no 7,8,9
10(3) = {127/136/145/235}, no 8,9
11(3) = {128/137/146/236/245}, no 9
12(3) = {129/138/147/156/237/246/345}
13(3) = {139/148/157/238/247/256/346}
14(3) = {149/158/167/239/248/257/347/356}
15(3) = {159/168/249/258/267/348/357/456}
16(3) = {169/178/259/268/349/358/367/457}
17(3) = {179/269/278/359/368/458/467}
18(3) = {189/279/369/378/459/468/567}
19(3) = {289/379/469/478/568}, no 1
20(3) = {389/479/569/578}, no 1,2
21(3) = {489/579/678}, no 1,2,3
22(3) = {589/679}
23(3) = {689}
24(3) = {789}
4-cell cages10(4) = {1234}
11(4) = {1235}
12(4) = {1236/1245}, no 7,8,9
13(4) = {1237/1246/1345}, no 8,9
14(4) = {1238/1247/1256/1346/2345}, no 9
15(4) = {1239/1248/1257/1347/1356/2346}
16(4) = {1249/1258/1267/1348/1357/1456/2347/2356}
17(4) = {1259/1268/1349/1358/1367/1457/2348/2357/2456}
18(4) = {1269/1278/1359/1368/1458/1467/2349/2358/2367/2457/3456}
19(4) = {1279/1369/1378/1459/1468/1567/2359/2368/2458/2467/3457}
20(4) = {1289/1379/1469/1478/1568/2369/2378/2459/2468/2567/3458/3467}
21(4) = {1389/1479/1569/1578/2379/2469/2478/2568/3459/3468/3567}
22(4) = {1489/1579/1678/2389/2479/2569/2578/3469/3478/3568/4567}
23(4) = {1589/1679/2489/2579/2678/3479/3569/3578/4568}
24(4) = {1689/2589/2679/3489/3579/3678/4569/4578}
25(4) = {1789/2689/3589/3679/4579/4678}
26(4) = {2789/3689/4589/4679/5678}, no 1
27(4) = {3789/4689/5679}, no 1,2
28(4) = {4789/5689}, no 1,2,3
29(4) = {5789}
30(4) = {6789}
5-cell cages15(5) = {12345}
16(5) = {12346}
17(5) = {12347/12356}, no 8,9
18(5) = {12348/12357/12456}, no 9
19(5) = {12349/12358/12367/12457/13456}
20(5) = {12359/12368/12458/12467/13457/23456}
21(5) = {12369/12378/12459/12468/12567/13458/13467/23457}
22(5) = {12379/12469/12478/12568/13459/13468/13567/23458/23467}
23(5) = {12389/12479/12569/12578/13469/13478/13568/14567/23459/23468/23567}
24(5) = {12489/12579/12678/13479/13569/13578/14568/23469/23478/23568/24567}
25(5) = {12589/12679/13489/13579/13678/14569/14578/23479/23569/23578/24568/34567}
26(5) = {12689/13589/13679/14579/14678/23489/23579/23678/24569/24578/34568}
27(5) = {12789/13689/14589/14679/15678/23589/23679/24579/24678/34569/34578}
28(5) = {13789/14689/15679/23689/24589/24679/25678/34579/34678}
29(5) = {14789/15689/23789/24689/25679/34589/34679/35678}
30(5) = {15789/24789/25689/34689/35679/45678}
31(5) = {16789/25789/34789/35689/45679}
32(5) = {26789/35789/45689}, no 1
33(5) = {36789/45789}, no 1,2
34(5) = {46789}
35(5) = {56789}
6-cell cages21(6) = {123456}
22(6) = {123457}
23(6) = {123458/123467}, no 9
24(6) = {123459/123468/123567}
25(6) = {123469/123478/123568/124567}
26(6) = {123479/123569/123578/124568/134567}
27(6) = {123489/123579/123678/124569/124578/134568/234567}
28(6) = {123589/123679/124579/124678/134569/134578/234568}
29(6) = {123689/124589/124679/125678/134579/134678/234569/234578}
30(6) = {123789/124689/125679/134589/134679/135678/234579/234678}
31(6) = {124789/125689/134689/135679/145678/234589/234679/235678}
32(6) = {125789/134789/135689/145679/234689/235679/245678}
33(6) = {126789/135789/145689/234789/235689/245679/345678}
34(6) = {136789/145789/235789/245689/345679}
35(6) = {146789/236789/245789/345689}
36(6) = {156789/246789/345789}
37(6) = {256789/346789}, no 1
38(6) = {356789}
39(6) = {456789}
7-cell cages28(7) = {1234567}
29(7) = {1234568}
30(7) = {1234569/1234578}
31(7) = {1234579/1234678}
32(7) = {1234589/1234679/1235678}
33(7) = {1234689/1235679/1245678}
34(7) = {1234789/1235689/1245679/1345678}
35(7) = {1235789/1245689/1345679/2345678}
36(7) = {1236789/1245789/1345689/2345679}
37(7) = {1246789/1345789/2345689}
38(7) = {1256789/1346789/2345789}
39(7) = {1356789/2346789}
40(7) = {1456789/2356789}
41(7) = {2456789}
42(7) = {3456789}
8-cell cages36(8) = {12345678}
37(8) = {12345679}
38(8) = {12345689}
39(8) = {12345789}
40(8) = {12346789}
41(8) = {12356789}
42(8) = {12456789}
43(8) = {13456789}
44(8) = {23456789}
and finally45(9) = {123456789}